A solid has square cross sections taken perpendicular to the -axis
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A solid has square cross sections taken perpendicular to the x-axis. Its base is the region in the first quadrant bounded by the x-axis, the y-axis, and the graph of y=x for 0≤x≤4.
(a) Express the side length of a typical square cross section as a function of x on the interval [0,4]. Simplify your expression.
(b) Set up, but do not yet evaluate, a definite integral for the volume of the solid.
(c) Evaluate the integral obtained in part (b) to determine the volume. Present exact values and include appropriate units.
(d) Interpret the meaning of the numerical value you obtained in part (c) in terms of the dimensions given for the solid.