CPM Homework Help : APCALC Problem 8-127

Multiple Choice: The base of a solid is a region in the first quadrant under the curve $f ( x ) = \sqrt { 4 - x }$ , as shown in the diagram at right. The cross-sections of the solid are squares perpendicular to the $x$ -axis. What is the volume of the solid?

$\frac { 16 } { 3 }$

$\frac { 64 } { 9 }$

$8π$

$\frac { 16 \pi } { 3 }$

First quadrant decreasing concave down curve, starting at the point (0 comma 2), stopping at the point (4, comma 0), shaded region under the curve, above x axis, & right of y axis.

Hint:

$\text{volume by cross-sections }=\int_{x=a}^{x=b}(\text{area function})dx$