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Trigonometry and Geometry Exam – Review CEINSTRUCTIONS: Solve the following problems correctly with complete solution. Write the letter of the correct answer before each number.1. If the cosine of angle x is 3/5, then the value of the sine of x/2 is a. 0 b. 0 c. 0 d. 0. 2. If 82 0 + 0 = Arctan(cot 0...

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T r i gonome t r ya ndGe ome t r yEx a m–Re v i e wCE I NST RUCT I ONS: So l v et h ef o l l o wi n gp r o b l e msc o r r e c t l ywi t hc o mp l e t es o l u t i o n . Wr i t et h el e t t e ro f t h ec o r r e c t a n s we rb e f o r ee a c h n u mb e r . 1 .I f t h ec o s i n eo f a n g l exi s3 / 5 , t h e nt h ev a l u eo f t h es i n eo f x / 2i s a . 0 . 5 0 0 b . 0 . 3 6 1 c . 0 . 2 1 5 d . 0 . 4 4 7 0 2 .I f 8 2 +0 . 3 5 x=Ar c t a n ( c o t 0 . 4 5 x ) , fi n dx . a . 1 1 d e g b . 1 0 d e g c . 1 2 d e g d . 1 3 d e g 3 .I f s e cA=5 / 4 , Ai nq u a d r a n t I I , fi n dt a n2 A. a . 2 4 / 7 b . 2 5 / 7 c . 2 5 / 7 d . 2 4 / 7 4 .I f y s i n x=aa n dy c o s x=b , fi n dyi nt e r mso f aa n db . 2 a . a+b b . a2+b c . 5 .I f t a n ( Ar c t a n x+Ar c t a n¼) =7 / 1 1 , fi n dx . a . 1 / 3 b . ¼ c . 1 / 5

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6 .I f tan θ=√ 3 , θi nq u a d r a n t I I I , fi n dt h ev a l u eo f . a . ½ b . ¼ c . 1 / 3 d . 1 / 5 7 .T wob u i l d i n g swi t hfl a t r o o f sa r e1 5ma p a r t . F r o mt h ee d g eo f t h er o o f o f t h el o we rb u i l d i n g s , t h ea n g l eo f e l e v a t i o no f t h e e d g eo f t h er o o f o f t h et a l l e rb u i l d i n gi s3 2d e g r e e s . Ho wh i g hi st h et a l l e rb u i l d i n gi f t h el o we rb u i l d i n gi s1 8mh i g h ? a . 2 6 . 4m b . 2 7 . 4m c . 2 8 . 4m d . 2 9 . 4m n d2 θi nq u a d r a n t I V . 8 . Gi v e n : s e c2 θ= √ 10 a Fi n d : c o s4 θ a . 0 . 6 0 b . 0 . 7 0 c . 0 . 8 0 d . 0 . 9 0 0 0 0 9 . Th eb e a r i n go f Bf r o mAi nN2 0 E, t h eb e a r i n go f Cf r o mBi sS3 0 Ea n dt h eb e a r i n go f Af r o mCi sS4 0 W. I f AB=1 0 , fi n dt h e a r e ao f t r i a n g l eABC. a . 1 4 . 9 5 b . 1 3 . 9 4 c . 1 2 . 9 3 d . 1 1 . 9 2 1 0 .T wos h i p ss t a r t f r o mt h es a mep o i n t , o n eg o i n gs o u t ha n dt h eo t h e rNo r t h2 8d e g r e eEa s t . I f t h es p e e do f t h efi r s t s h i pi s1 2 k p ha n dt h es e c o n ds h i pi s1 6k p h , fi n dt h ed i s t a n c eb e t we e nt h e ma f t e r4 5mi n u t e s . a . 1 7 . 3k m b . 1 8 . 5k m c . 1 9 . 2k m d . 2 0 . 4k m 1 1 .Fi n dt h eh e i g h t o f at r e ei f t h ea n g l eo f e l e v a t i o n so f i t st o pc h a n ge sf r o m2 0d e g r e e st o4 0d e g r e e sa st h eo b s e r v e ra d v a n c e s 2 3mt o wa r di t sb a s e . a . 1 3 8 . 5m b . 1 4 8 . 5m c . 1 5 8 . 5m d . 1 5 9 . 5m 1 2 .At r e es t a n d sv e r t i c a l l yo nah i l l s i d ewh i c hma k e sa na n g l eo f 2 2d e g r e e swi t ht h eh o r i z o n t a l . Fr o map o i n t 6 0f t d o wnt h eh i l l d i r e c t l yf r o mt h eb a s eo f t h et r e e , t h ea n g l eo f e l e v a t i o no f t h et r e e , t h ea n g l eo f e l e v a t i o no f t h et o po f t h et r e ei s5 5d e g r e e . Ho wh i g hi st h et r e e ? a . 5 6 . 9 7f t b . 5 7 . 9 6f t c . 5 9 . 7 6f t d . 5 7 . 6 9f t fi n dc o s 8 A. 1 3 .I f c o s 2 A= √ m , a . 8 m2+8 m+1 b . 8 m2+8 m–1c . 8 m2–8 m+1d . 8 m2–8 m-1 1 4 .Th ea n g l e so f t r i a n g l eABCa r ei nt h er a t i o5 : 1 0 : 2 1a n dt h es i d eo p p o s i t et h es ma l l e s t a n g l ei s5 . Fi n dt h es i d eo p p o s i t et h e l a r g e s t a n g l e . a . 1 3 . 4 1 b . 1 4 . 3 1 c . 1 3 . 1 4 d . 1 1 . 4 3 1 5 .Ont o po f ac l i ff , t h ef a r t h e s t d i s t a n c et h a t c a nb es e e no nt h es u r f a c eo f t h ee a r t hi s6 0mi l e s . Ho wh i g hi st h ec l i ffi f t h e r a d i u so f t h ee a r t hi st a k e nt ob e4 , 0 0 0mi l e s ? a . 0 . 4 1mi b . 0 . 4 3mi c . 0 . 4 5mi d . 0 . 4 7mi 1 6 .T woo b s e r v e r s1 0 0ma p a r t a n df a c i n ge a c ho t h e ro nah o r i z o n t a l p l a n e , o b s e r v ea t t h es a met i met h ea n g l e so f e l e v a t i o no f ab a l l o o ni nt h e i rv e r t i c a l t ob e5 8d e g r e e sa n d4 4d e g r e e s . Fi n dt h eh e i gh t o f t h eb a l l o o n . a . 6 0 . 2 3m b . 5 9 . 3 4m c . 6 1 . 3 1m d . 5 8 . 7 5m 1 7 .F r o map o i n t o u t s i d ea ne q u i l a t e r a l t r i a n g l e , t h ed i s t a n c eo f t h ev e r t i c e sa r e1 0m, 1 8ma n d1 0mr e s p e c t i v e l y . Fi n dt h es i d e o f t h et r i a n g l e . a . 1 9 . 9 4m b . 2 0 . 9 4m c . 2 1 . 9 4m d . 2 2 . 9 4m

1 8 .Si mp l i f y a . c s cA b . s e cA c . c o t A d . s i nA 1 9 .I f c o s ( x+y )=0 . 1 7a n dc o s x=0 . 5 0 , fi n ds i n y . a . 0 . 2 3 5 5 b . 0 . 3 4 5 5 c . 0 . 4 3 4 4 d . 0 . 4 2 3 3 2 0 .I f s i n A+s i n B=1a n ds i nA–s i nB=1 , fi n dA. a . 6 0 d e g b . 7 0 d e g c . 8 0 d e g d . 9 0 d e g 2 1 .Fi n dt h es u mo f a l l t h ea c u t ei n t e r i o ra n g l e so f ar e g u l a rh e x a g o n . a .7 2 0 ˚ c . 3 6 0 ˚ b.5 4 0 ˚ d . 2 7 0 ˚ 2 2 .Fi n dt h ea r e ao f ar e g u l a rh e x a g o no f s i d e3c m. a . 2 2 . 2 8c m2b . 2 3 . 3 8c m2 c . 2 4 . 4 8c m2 d . 2 5 . 5 8c m2 2 3 .At r i a n g l eh a ss i d e s3 , 6a n d9 . Fi n dt h es h o r t e s t s i d eo f as i mi l a rt r i a n g l ewh o s el o n g e s t s i d ei s1 5 . a . 6 b . 1 0 c . 8 d . 5 2 4 .Th ep e r i me t e r o f a no c t a g o ni s3 2a n di t sl o n g e s t s i d ei s6 . Wh a t i st h el o n g e s t s i d eo f as i mi l a ro c t a g o nwh o s ep e r i me t e ri s 2 4 ? a . 3 . 5 b . 4 c . 4 . 5 d . 5 2 5 .Ah e x a g o ni sc i r c u ms c r i b e da b o u t ac i r c l eo f r a d i u s5 . I f t h ep e r i me t e ro f t h eh e x a g o ni s3 8 , wh a t i st h ea r e ao f t h eh e x a g o n ? a . 7 5 b . 6 5 c . 8 5 d . 9 5 2 6 .I f ar e g u l a rp o l y g o nh a s5 4d i a g o n a l s , t h e ni t h a sh o wma n ys i d e s ? a . 1 0 b . 1 1 c . 1 4 d . 1 2 2 7 .Wh a t i st h ed i a me t e ro f ac i r c l et h a t i sc i r c u ms c r i b e da b o u t a ne q u i l a t e r a l t r i a n g l eo f s i d e7 . 4c m? a . 8 . 6 4c m b . 8 . 5 4c m c . 9 . 5 4c m d . 9 . 6 4c m 2 8 .Fi n dt h ea r e ao f ar e g u l a ro c t a g o ni n s c r i b e di nac i r c l ewh o s er a d i u si s1 0c m. a . 8 2 2 . 8c m2b . 2 8 2 . 8c m2 c . 8 2 8 . 2c m2 d . 2 2 8 . 8c m2 2 9 .I f t h ep e r i me t e ro f ar e g u l a r h e x a g o ni s2 4 , wh a t i si t sa p o t h e m?

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b .4 3 c .2 3 d .5 3 a .3 3 3 0 .Th er a t i oo f t h es u mo f t h ee x t e r i o ra n g l e st ot h es u mo f t h e s ei n t e r i o ra n g l e so f ap o l y g o ni s1 . 3 . I d e n t i f yt h ep o l y g o n . a . h e x a g o n b . h e p t a g o n c . o c t a g o n d . n o n a g o n 3 1 .Ac i r c u l a rs e c t o rh a sar a d i u so f 6c ma n dwh o s ec e n t r a l a n g l ei s6 0d e g r e e s . I f i t i sb e n t t of o r mar i g h t c i r c u l a rc o n e , t h e r a d i u so f t h ec o n ei s a . 1c m b . 2c m c . 3c m d . 4c m 3 2 .Ar e g u l a ro c t a g o ni si n s c r i b e di nac i r c l eo f r a d i u s6 . Fi n dt h ep e r i me t e ro f t h eo c t a g o n . a . 3 4 . 5 4 b . 3 5 . 6 4 c . 3 6 . 7 4 d . 3 7 . 8 4 0 0 3 3 .I f f o u ra n g l e so f ap e n t a g o nh a v eme a s u r e s1 0 00, 9 6 , 8 7 a n d9 70, fi n dt h eme a s u r eo f t h efi f t ha n g l e . a . 1 5 0 d e g b . 1 6 0 d e g c . 1 4 0 d e g d . 1 3 0 d e g 3 4 .I f t h es u mt woe x t e r i o ra n g l e so f at r i a n g l ei s2 3 00, fi n dt h eme a s u r eo f t h et h i r de x t e r i o ra n g l e . a . 1 3 0 d e g b . 1 2 0 d e g c . 1 1 0 d e g d . 1 0 0 d e g 3 5 .Ac i r c l ewh o s er a d i u si s1 0c mi si n s c r i b e di nar e g u l a rh e x a g o n . Th ea r e ao f t h eh e x a g o ni s a . 3 4 6 . 4c m2b . 6 3 4 . 4c m2 c . 3 6 4 . 4c m2 d . 4 3 6 . 6c m2 3 6 .As i d eo f ar e g u l a rh e x a g o ni s6 . Wh a t i st h ec i r c u mf e r e n c eo f i t sc i r c u ms c r i b e dc i r c l e ? a . 1 2p i b . 1 1p i c . 1 3p i d . 1 0p i 3 7 .T woc h o r d sPQa n dRSo f ac i r c l eme e t wh e ne x t e n d e dt h r o u g hQa n dSa t ap o i n t T . I f QP=7 , TQ=9 , TS=6 , fi n dSR. a . 1 6 b . 1 7 c . 1 8 d . 1 9 3 8 .Wh a t i st h ea n g l ea t c e n t e ro f ac i r c l ei f t h es u b t e n d i n gc h o r di se q u a l t ot wot h i r d so f t h er a d i u s ? a . 3 9 . 9 5 d e g b . 3 8 . 9 4 d e g c . 3 7 . 9 3 d e g d . 3 6 . 9 2 d e g 0 3 9 .Th ea r e ao f ar h o mb u si s2 5 0a n do n eo f t h ea n g l e si s3 7 2 5 ’ . Wh a t i st h el e n g t ho f e a c hs i d e ? a . 2 0 . 1 8 b . 2 0 . 2 8 c . 2 0 . 3 8 d . 2 0 . 4 8 0 0 4 0 .I f i nt r i a n g l eABC, A=7 6 3 0 ’ B=8 1 4 0 ’ a n dc=3 6 8 , fi n dt h ed i a me t e ro f t h ec i r c u ms c r i b e dc i r c l e . a . 9 8 9 . 5 b . 9 5 9 . 8 c . 9 9 5 . 8 d . 9 5 8 . 9 4 1 .Gi v e nap a r a l l e l o g r a mABCDs u c ht h a t AB=7 , AC=1 0a n da n g l eBAC=3 600 7 ’ . Fi n dt h el e n g t ho f BC.

a . 4 . 9 9 2 b . 5 . 9 9 2 c . 6 . 9 9 2 d . 7 . 9 9 2 4 2 .Wh a t i st h ed i a me t e ro f t h ec i r c l et h a t i sc i r c u ms c r i b e da b o u t a ni s o s c e l e st r i a n g l ewh o s ev e r t i c a l a n g l ei s8d e g r e e sa n dt h e s u mo f t h et woe q u a l s i d e s1 8u n i t s ? a . 7 . 1 1 b . 8 . 1 1 c . 9 . 1 1 d . 1 0 . 1 1 0 4 3 .Th ed i a g o n a l so f aq u a d r i l a t e r a l a r e3 4a n d5 6i n t e r s e c t i n ga t a na n g l eo f 6 7 . Fi n di t sa r e a . a . 8 3 7 . 6 2 b . 8 6 3 . 7 2 c . 8 2 6 . 3 7 d . 8 7 6 . 3 2 4 4 .Fi n dt h er a d i u so f ac i r c l ei nwh i c hi si n s c r i b e dar e g u l a r n o n a g o nwh o s ep e r i me t e ri s4 1 7 . 6c m a . 6 8 . 3 7c m b . 6 7 . 8 3c m c . 6 3 . 8 7c m d . 6 8 . 7 3c m 4 5 .I f e a c hi n t e r i o ra n g l eo f ar e g u l a rp o l y g o nh a same a s u r eo f 1 6 0 d e g r e e s , h o wma n ys i d e sh a st h ep o l y g o n ? a . 1 6 b . 1 7 c . 1 9 d . 1 8 4 6 .Th es i d e so f ar i g h t t r i a n g l ea r ea , b , a n dcwh e r eci st h eh y p o t e n u s e . Fi n dt h er a d i u so f t h ec i r c l et h a t i si n s c r i b e di nt h e t r i a n g l e . a . ½( a+b+c ) b . ½( a+b–c )c . ½( a–b+c )d . ½( a–b–c ) 4 7 .T wos i d e so f ap a r a l l e l o g r a ma r e2 0a n d3 0a n dt h ei n c l u d e da n g l ei s3 6d e g r e e s . Fi n dt h el e n g t ho f t h el o n ge rd i a g o n a l . a . 7 4 . 6 5 b . 6 4 . 7 5 c . 5 7 . 4 6 d . 4 7 . 6 5 4 8 .Th es i d e so f at r i a n g l ea r e1 7 , 2 1a n d2 8 . Fi n dt h el e n g t ho f t h el i n es e g me n t b i s e c t i n gt h el o n g e s t s i d ea n dd r a wnf r o mt h e o p p o s i t ea n g l e . a . 1 1 b . 1 2 c . 1 3 d . 1 4 4 9 .Ab r i d g ea c r o s sar i v e ri si nt h ef o r mo f a na r co f ac i r c u l a r . I f t h es p a ni s4 0f t a n dt h emi d p o i n t o f t h ea r ci st ob e8f t h i g h e r t h a nt h ee n d s , wh a t i st h er a d i u so f t h ec i r c l e ? a . 2 7 f t b . 2 8 f t c . 2 9 f t d . 3 0 f t 5 0 .Fi n dt h ea n g l ef o r me db yt h es e c a n t a n dt a n g e n t t oac i r c l ei f o n ei n t e r c e p t e da r ci s3 0d e g r e e smo r et h a nt h eo t h e ra n dt h e s e c a n t p a s s e st h r o u g ht h ec e n t e ro f t h ec i r c l e . a . 1 5 d e g b . 1 6 d e g c . 1 7 d e g d . 1 8 d e g 5 1 .Fi n dt h er a d i u so f ac i r c l ewh o s ea r e ai se q u a l t ot h ea r e ao f t h ea n n u l u sf o r me db yt woc o n s e c u t i v ec i r c l e swi t hr a d i i 5a n d 1 3 . a . 1 0 b . 1 1 c . 1 2 d . 1 3 5 2 .Ac i r c l ei si n s c r i b e di na ne q u i l a t e r a l t r i a n g l e . I f t h ec i r c u mf e r e n c eo f t h ec i r c l ei s3 , fi n dt h ep e r i me t e ro f t h ee q u i l a t e r a l t r i a n g l e . a . 9 . 2 4 6 b . 6 . 2 9 4 c . 2 . 9 4 6 d . 4 . 9 6 2 5 3 .Th eq u a d r i l a t e r a l ABCDi si n s c r i b e di nac i r c l ea n di t sd i a g o n a l ACi nd r a wns ot h a t a n g l eDAC=3 4d e g r e e s , a n g l eCAB=3 8 d e g r e e sa n da n g l eDBA=6 5d e g r e e s . Fi n da r eAB. 0 0 0 a . 9 6 b . 8 6 c . 7 60 d . 6 6 5 4 .As e c a n t a n dat a n g e n t t oac i r c l ei n t e r s e c t a na n g l eo f 3 8d e g r e e s . I f t h eme a s u r e so f t h ea r ci n t e r c e p t e db e t we e nt h e s e c a n t a n dt h et a n g e n t a r ei nt h er a t i o2 : 1 , fi n dt h eme a s u r eo f t h et h i r da r c . a . 1 2 9 d e g b . 1 3 0 d e g c . 1 3 1 d e g d . 1 3 2 d e g 5 5 .Co mp u t et h ed i ff e r e n c eb e t we e nt h ep e r i me t e r so f ar e g u l a rp e n t a g o na n dar e g u l a rh e x a g o ni f t h ea r e ao f e a c hi s1 2 . a . 0 . 3 1 b . 0 . 2 1 c . 0 . 4 1 d . 0 . 5 1 5 6 .Th ea r e ao f t h es e c t o ro f ac i r c l eh a v i n gac e n t r a l a n g l eo f 6 0d e g r e e si s2 4Π . Fi n dt h ep e r i me t e ro f t h es e c t o r . a . 3 4 . 4 b . 3 5 . 5 c . 3 6 . 6 d . 3 7 . 7 5 7 .Fi n dt h ec o mmo na r e ao f t woi n t e r s e c t i n gc i r c l e so f r a d i i 1 2a n d1 8r e s p e c t i v e l yi f t h e i rc o mmo nc h o r di s1 4l o n g . a . 3 4 . 1 9 b . 3 5 . 2 9 c . 3 6 . 3 9 d . 3 4 . 7 9 5 8 .I f t h es i d e so f a ne q u i l a t e r a l t r i a n g l ea r ei n c r e a s e db y2 1%, b yh o wmu c hi si t sa r e ai n c r e a s e d ? a .3 3 . 1% c . 1 0% b.7 7 . 2% d . 4 6 . 4% 5 9 .Th es u mo f t h es i d e so f at r i a n g l ei s1 0 0 . Th ea n g l ea t Ad o u b l et h a t o f Ba n dt h ea n g l ea t Bi sd o u b l et h a t o f C. Fi n ds i d ec . a . 4 0 b . 2 5 c . 5 2 d . 5 0 9 0 0 6 0 .Ad i a g o n a l o f ap a r a l l e l o g r a mi s5 6 . 3 8f t l o n ga n dma k e sa na n g l eo f 2 7 1 3 ’ a n d1 6 2 4 ’ r e s p e c t i v e l ywi t ht h es i d e s . Fi n dt h e a r e ao f t h ep a r a l l e l o g r a m 2 2 2 2 a . 5 9 5f t b . 5 8 5f t c . 5 7 5f t d . 5 6 5f t 6 1 .Fi n dt h ea r e ao f ar e g u l a rfi v ep o i n t e ds t a rt h a t i si n s c r i b e di nac i r c l eo f t h er a d i u s1 0 . a . 1 2 1 . 6 2 b . 1 1 2 . 2 6 c . 1 2 2 . 1 6 d . 1 2 6 . 2 1

6 2 .Wh a t i st h ed i ff e r e n c ei nt h ea r e a sb e t we e na ni n s c r i b e da n dac i r c u ms c r i b e dr e g u l a ro c t a g o ni f t h er a d i u so f t h ec i r c l ei s6 ? a . 1 5 . 2 7 b . 1 6 . 3 7 c . 1 7 . 4 7 d . 1 8 . 5 7 6 3 .As s u mi n gt h a t t h ee a r t hi sap e r f e c t s p h e r eo f r a d i u s6 , 3 7 0k i l o me t e r s , ap e r s o na t ap o i n t To nt o po f at o we r6 0me t e r sh i g h l o o k sa t ap o i n t Po nt h es u r f a c eo f t h ee a r t h . Wh a t i st h ea p p r o x i ma t ed i s t a n c eo f Pf r o mT? a . 2 4 . 3k m b . 2 5 . 4k m c . 2 6 . 5k m d . 2 7 . 6k m 6 4 .Th ea l t i t u d eo f ap a r a l l e l o g r a mi s2 0a n dt h eb a s ei sar h o mb u swi t hd i a g o n a l s1 0a n d1 6 . Fi n dt h ev o l u meo f t h e p a r a l l e l e p i p e d . a . 1 , 5 0 0 b . 1 , 6 0 0 c . 1 , 7 0 0 d . 1 , 8 0 0 6 5 .Awo o d e nc o n eo f a l t i t u d e1 0c mi st ob ec u t i n t ot wop a r t so f e q u a l we i g h t . Ho wf a rf r o mt h ev e r t e xs h o u l dt h ec u t p a r a l l e l t o t h eb a s eb ema d e ? a .6 . 6 5c m c . 7 . 9 4c m b .3 . 8 3c m d . 8 . 8 3c m 6 6 .Fi n dt h ev o l u meo f ap y r a mi dh a v i n gap e n t a g o n a l b a s ewi t hs i d e se a c he q u a l t o1 2c ma n da na p o t h e mo f 8c m. Th ea l t i t u d e o f t h ep y r a mi di s3 6c m. a . 2 , 6 6 0c m3 b . 2 , 7 7 0c m3 c . 2 , 8 8 0c m3 d . 2 , 9 9 0c m3 6 7 .Ar e g u l a rt r i a n g l ep y r a mi dh a sa na l t i t u d eo f 9ma n dav o l u meo f 1 8 7 . 0 6c u . m. Wh a t i st h eb a s ee d g ei nme t e r s ? a .1 0 c . 1 2 b.1 1 d . 1 3 6 8 .Th el a t e r a l a r e ao f ar i g h t c i r c u l a rc o n ewi t har a d i u so f 2 0c ma n dah e i g h t o f 3 0c mi s a . 2 , 2 6 5 . 4 3c m2 b . 2 , 2 3 6 . 4 5c m2 c . 2 , 2 4 5 . 6 3c m2 d . 2 , 2 5 3 . 4 6c m2 6 9 .Th eb a s eo f ap r i s mi sar e c t a n g l ewi t hs i d e s3a n d5 . I f i t sl a t e r a l a r e ai s6 4 , fi n di t sa l t i t u d e . a . 3 b . 4 c . 5 d . 6 7 0 .Fi n dt h en u mb e ro f d e g r e e so nad i h e d r a l a n g l eo f ar e g u l a rt e t r a h e d r o n . 0 0 0 a . 6 8 . 3 3 b . 6 9 . 4 30 c . 7 0 . 5 3 d . 7 1 . 6 3 7 1 .Fi n dt h ev o l u meo f as p h e r i c a l z o n ei nas p h e r eo f r a d i u s1 7c mi f t h er a d i u so f t h ez o n ei s8c m. 3

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b . 1,136 Π /3 cm c . 1,146 Π /3 cm d . 1,156 Π /3 cm a . 1,126 Π /3 cm 7 2 .Fi n dt h ev o l u meo f at r i a n g u l a rp r i s mwh o s ea l t i t u d ei s2 0c ma n dwh o s es i d e sa r e6c m, 8c ma n d1 2c m. a . 4 2 6 . 6 1c m3 b . 4 2 1 . 6 6c m3 c . 4 6 1 . 2 6c m3 d . 4 1 6 . 6 2c m3 7 3 .Fi n dt h ev o l u meo f as p h e r i c a l s e g me n t i f t h er a d i i o f t h eb a s e sa r e3a n d4r e s p e c t i v e l ya n di t sa l t i t u d ei s2 . a . 8 3 . 2 7 b . 8 7 . 3 2 c . 8 3 . 7 2 d . 8 2 . 7 3 7 4 .I f t h ee d g eo f ac u b ed e c r e a s e db yx%, i t sv o l u med e c r e a s e db y4 8 . 8 %. Fi n dt h ev a l u eo f x . a .1 0 c . 1 6 b.2 0 d . 2 5 7 5 .Th eb a s eo f ar i g h t p a r a l l e l e p i p e di sar h o mb u swh o s es i d e sa r ee a c h1 0c ml o n ga n do n eo f wh o s ea n g l e si s6 0d e g r e e s . I f t h ea l t i t u d eo f t h ep a r a l l e l e p i p e di s4c m, fi n di t sv o l u me . 3

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a . 100 √ 3cm b . 200√ 3 cm c . 300√3cm d . 400√ 3cm 7 6 .Fi n dt h ev o l u meo f t h el a r g e s t c u b et h a t c a nb eo u t f r o mac i r c u l a rl o gwh o s er a d i u si s3 0 . a . 7 6 , 3 6 7 . 5 3 b . 7 5 , 5 6 7 . 3 3 c . 7 3 , 6 7 5 . 3 6 d . 7 7 , 6 5 3 . 3 6 7 7 .Fi n dt h el a t e r a l a r e ao f ap y r a mi dwh o s ea l t i t u d ei s2 7c ma n dwh o s eb a s ei sas q u a r e8c mo nas i d e . a . 4 3 7 . 6 2c m2 b . 4 3 6 . 7 2c m2 c . 4 3 2 . 7 6c m2 d . 4 2 7 . 6 3c m2 7 8 .Th eb a s eo f ac y l i n d e ri sah e x a g o ni n s c r i b e di nac i r c l e . I f t h ed i ff e r e n c ei nc i r c u mf e r e n c eo f t h ec i r c l ea n dp e r i me t e ro f t h e h e x a g o ni s4c m. , fi n dt h ev o l u meo f t h ec y l i n d e ri f i t h a sa na l t i t u d eo f 2 0 c m. a .1 0 3 6 7c m³ c . 1 0 1 2 3c m³ b.1 2 2 3 9c m³ d . 1 1 2 3 1c m³ 7 9 .Fi n dt h el a t e r a l a r e ao f t h ef r u s t u mo f ar e g u l a rs q u a r ep y r a mi dwh o s eb a s ee d g e sa r e6a n d1 2a n dwh o s ea l t i t u d ei s4 . a . 1 5 0 b . 1 6 0 c . 1 7 0 d . 1 8 0 8 0 .I f t h er a d i u so f as p h e r ei s8a n di f ap l a n ep a s s e st h r o u g ht h es p h e r e sa t ad i s t a n c eo f 5f r o mi t sc e n t e r , wh a t a r et h ea r e a s o f t h ec i r c l eo f i n t e r s e c t i o n ? a . 3 8p i b . 3 9p i c . 4 0p i d . 4 1p i 8 1 .Fi n dt h el a t e r a l a r e ao f ar i g h t c i r c u l a rc o n et h a t c o n et h a t c a nb ei n s c r i b e di nac u b ewh o s ev o l u mei s6 4 . a . 2 8 . 1 b . 2 6 . 1 c . 2 4 . 1 d . 2 2 . 1

8 2 .Fi n dt h el a t e r a l e d g eo f ar e g u l a rs q u a r ep y r a mi dwh o s es l a n t h e i gh t i s8a n dwh o s eb a s ee d g ei s6 . a . 6 . 5 4 b . 7 . 5 4 c . 8 . 5 4 d . 9 . 5 4 8 3 .Th eb a s ee d g e so f at r i a n g u l a rp y r a mi da r e1 2 , 1 4a n d1 6 . I f i t sa l t i t u d ei s2 2 , wh a t i st h ev o l u meo f t h ep y r a mi d ? a . 5 9 4 . 6 4 b . 5 6 4 . 9 4 c . 5 4 4 . 6 9 d . 5 9 6 . 4 4 8 4 .Th ev o l u meo f t h ef r u s t u mo f ar i g h t c i r c u l a r c o n ei s7 8p i . Th eu p p e rb a s er a d i u si s2a n dt h el o we rb a s er a d i u si s5 . Wh a t i s t h ea l t i t u d eo f t h ef r u s t u m? a . 5 b . 6 c . 7 d . 8 8 5 .Th ev o l u meo f ar i g h t c i r c u l a rc o n eh a v i n gas l a n t h e i g h t o f 1 3a n da l t i t u d e1 2i s a . 100Π b . 150Π c . 200 Π d . 250 Π 8 6 .Fi n dt h eh e i g h t o f ap y r a mi dwh o s ev o l u mei s3 5a n dwh o s eb a s ei sat r i a n g l ewi t hs i d e s4 , 7a n d5 . a . 1 1 . 7 2 b . 1 0 . 7 2 c . 8 . 7 2 d . 9 . 7 2 8 7 .Th er a d i i o f t h eb a s e so f t h ef r u s t u mo f ar i g h t c i r c u l a rc o n ea r e6a n d9r e s p e c t i v e l ya n di t sa l t i t u d ei s4 . Fi n di t sl a t e r a l a r e a . 75Π 85 Π 95 Π 65 Π b . c . d . a . 8 8 .Ac i r c l ei si n s c r i b e di nas q u a r eo f s i d e1 0m. As ma l l c i r c l ee x t e r n a l l yt a n g e n t t ot h ei n s c r i b e dc i r c l ei ss i t u a t e ds u c ht h a t t wo s i d e so f t h es q u a r ea r et a n g e n t t oi t . De t e r mi n et h ed i a me t e ro f t h es ma l l c i r c l e . a .0 . 4 2 9m c . 1 . 7 1 6m b.0 . 8 5 8m d . 2 . 1 4 5m 8 9 .Wh a t i st h ea r e ao f as p h e r ei f az o n eo ni t h a v i n ga na r e ao f 18Π , h a sa na l t i t u d eo f 2 ? a . 7 9p i b . 8 0p i c . 8 1p i d . 8 2p i 9 0 .As p h e r i c a l b o wl o f r a d i u s8i n c h e ...