A student is asked to find the volume of a solid whose cross sections perpendicular…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A student is asked to find the volume of a solid whose cross sections perpendicular to the

y

-axis are squares. The solid sits on the region in the first quadrant bounded by the

y

-axis, the

x

-axis, and the curve

y=6-x^{2}

. The student proposes the following integral:

V=\int_{0}^{6} \left(6-y\right)^{2} \, dy.

(a) Identify and explain every error in the student’s integral set-up. (b) Write the corrected definite integral that represents the volume of the solid, justifying each component of your expression (integrand, limits, and differential).

Related theory

Area Applications
Volume Applications
Applications of Integration

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