AP Calculus ABmediummcq1 pt

The base of a solid is the region bounded by the graph of y=xy=\sqrt{x}, the xx-axis, and the line x=4x=4. Cross sections perpendicular to the xx-axis are squares. What is the volume of the solid?

A.163\frac{16}{3}
B.643\frac{64}{3}
C.88
D.44

Explanation

Core Concept

Each square has side x\sqrt{x}, so its area is xx. The volume is 04xdx=[x22]04=8\int_0^4 x\,dx=[\frac{x^2}{2}]_0^4=8.

Correct Answer

C88

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