Victory for the ACT Exam 16e TG Sample

U NIT 4 | G EOMETRY • 521

STUDENT TEXT, p. 190 27. Wi n hs aqtuiasr tehien cahpepsr,ooxfi ma ba tael l swu ri tfha cae laarregae,s t circumference of 12 r inches? ( 4 SA r 2 = r Sphere ) A. 12 r B. 36 r C. 144 r D. 576 r r . If a cone has a height of 10 cm and a volume of 120 cm r 3 , what is the diameter of its base, in centimeters? F. 6 G. 12 H. J. 3 7 6 2 28. Tushiengvotlhuemfoeromf ualcaone can be found 3 1 V r h 2 =

EXPLANATIONS 27 . (C) Mathematics/Geometry/Solids CC: HSG-MG.A.1 CCRS: ADV.G.1 Difficulty Level = 3; Teaching Time = 3–6 minutes; Purpose = Example To �ind the surface area, �irst �ind

tchirecuramdfieurseonfctehoef sphere. Set the 12 r inches equal to the formula for circumference ( 2 05 C r = r ) and solve for r : 2 12 2 12 r r & & = = r r r 6 = . Ni not ow,t hs ue bf os trimt uut el a tfhoirs tvhael useu roffatcheearraedai uo sf a sphere: 4 r = r 2 4 144 6 . 2 ^ h Difficulty Level = 3; Teaching Time = 3–6 minutes; Purpose = Example Since V = 120 cm 3 r and h = 10, use the volume formula given ( 3 1 V r h 2 = r ) to �ind r : 3 1 120 3 1 10 V r h r 2 2 & = = r r r ^ h r 36 & = 2 r 06 = . Next, �ind the diameter: 6(2) = 12.

28 . (G) Mathematics/Geometry/Solids CC: HSG-MG.A.1 CCRS: ADV.G.1

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