AP Calculus AB 8.8 Volume with Cross Sections Question Bank

Practise volume questions by expressing cross-sectional area as a function and integrating over the stated interval.

Exam points

model cross-sectional area as a function of position
integrate cross-sectional area to find a solid’s volume

[Maximum number: 1]

The base of a solid is a right triangle with legs of length 6 and 16, as shown in the figure. The hypotenuse of the triangle is given by the line $y=-\frac{3}{8}(x-16)$ . Each cross section of the solid perpendicular to the x-axis is a semicircle. What is the volume of the solid?

398

796

593

186

Figure for Question CHA-5.B—Calculate volumes of solids with known cross sections using definite integrals—Topic 8.8 question 1 — AP Calculus AB

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CHA-5.B—Calculate volumes of solids with known cross sections using definite integrals—Topic 8.8 question 1