Let be the solid whose base is the triangular region in the first quadrant bounded by…

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

S

be the solid whose base is the triangular region in the first quadrant bounded by the

y

-axis, the line

y=3

, and the line

x=y

. For each

y

with

0\le y\le3

, the cross section of

S

taken perpendicular to the

y

-axis is a semicircle whose diameter lies in the base region. All coordinates are in centimeters. (a) Set up, but do NOT evaluate, a definite integral that gives the volume

V

of the solid

S

. Clearly express the diameter of the semicircle as a function of

y

. (b) Evaluate the integral from part (a) to obtain an exact value for

V

. Include correct units in your answer.

Related theory

Volume Applications
Applications of Integration

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