AP Calculus ABhardmcq1 pt

The base of a solid is the region bounded by the graph of y=x2y=x^2 and the line y=4y=4. Cross sections perpendicular to the yy-axis are squares. What is the volume of the solid?

A.2563\frac{256}{3}
B.3232
C.323\frac{32}{3}
D.1283\frac{128}{3}

Explanation

Core Concept

Each square has side 2y2\sqrt{y}, so its area is 4y4y. The volume is 044ydy=[2y2]04=32\int_0^4 4y\,dy=[2y^2]_0^4=32.

Correct Answer

B3232

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