For , a solid has identical rectangular cross sections of area square centimeters…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For 0<r<90<r<9, a solid has identical rectangular cross sections of area A(r)=3r (9−r)A(r)=3r\,(9-r) square centimeters throughout its 5-centimeter length. The volume of the solid is therefore V(r)=45r(9−r)V(r)=45r(9-r) cubic centimeters. Which value of rr maximizes the volume? (a) r=6r=6 (b) r=4.5r=4.5 (c) r=9r=9 (d) r=3r=3

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