The region under the curve for is the base of a solid

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The region under the curve

y=\sqrt{x}

for

0\le x\le 9

is the base of a solid. Rectangular cross sections are taken perpendicular to the

x

–axis; each rectangle has height

m

times its base (the base of the rectangle is the vertical segment from the curve to the

x

–axis). If the volume of the solid is

162

cubic units, what is the value of

m

? (a)

8

(b)

4

(c)

9

(d)

3