Question

A
solid has a circular base of radius 1. Its parallel cross-sections
perpendicular to the base are parabolas. The largest parabola has
the equation y = 4 − x ^2 if placed on the plane. What is the
volume?

A. 9π/2

B. 1/2

C. π/2

D. 9/2

E. None of these

Answer #1

Solution-

Use the volume by curve rotation,

Rotate the curve about the y-axis from 0 to 4 in x range (-1,1).

For the base radius r = 1

substitute the value for x2,

Therefore the volume of the curve rotation is

Correct answer : C

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