Victory for the ACT Exam 16e TG Sample

522 • M ATH

STUDENT TEXT, p. 190 29. AT hceo ns isl tor ui sc at i oc ynl icnodme pr awniyt hi sabhuei ml d ii snpghae sr ei l o . of ene tt oapn. dTthhee dhi ea img he tt eorf ot hf et hcey lciynldi nedr ei sr 4i s04 2 fseileot,. iHnocwubmicufceheth?ay can be stored in the

EXPLANATIONS

29 . (A) Mathematics/Geometry/Solids CC: HSG-MG.A.1 CCRS: EXP.G.2 Difficulty Level = 4; Teaching Time = 5–8 minutes; Purpose = Walkthrough Tt hhee ctyolti anldveor l pu ml u se ti hs et hveo vl uoml uemoef ot hf e hd ei ammi se pt ehreirse 4. A2 s, tfhoer rt ah de i cuysl ii ns d2e1r,, at hn ed the height is 40, so V r h 2 = = r cylinder 17,640 = r r 21 40 2 ^ h ^ h . Next, �ind the volume of the hemisphere by �inding the volume of a sphere and dividing by 2: 12,348 V r = = = r r r 3 4 3 4 21 3 3 sphere ^ h , so the volume of the hemisphere is 6,174 r . Therefore, the total volume of the silo is 17, 640 6, 174 23, 814 r r r .

A. 23,814 r B. 29,988 r C. 711,774 r D. 717,948 r

GEOMETRY STRATEGIES

TNho itse stehcatti ,oinn ignetnr oe dr aul c, et hs esseev ea rl tael ranl at et irvnea st itvr ea ttei mg i ee s- saarvei nbge ss tt rraetseegri ve es df of ro rs os li vt ui na gt i oGne so mi newt rhyi ci the m s . students are unable to solve a given item by directly applying the principles of geometry. So or m“ geutei ms set ismi taitsi npgo.”s sDi be ml e ot no satrrraitveetahti sa ccoonrcr ee pc tt abnysdwrearwsi inmg pt hl yebf yo lml oawkiinngg aanrgol ue sg:h a p p r o x i m a t i o n ,

“Guesstimating” Items #30–32

If students are able to visualize these angles successfully, they will be able to arrive at an accurate approximation of almost any angle (except in those special cases where �igures are not drawn to scale).