What is the volume of the solid generated when the region bounded by the graph of y=x^{2}, the vertical line x=3, and the horizontal line y=4 is revolved about the horizontal line y=4 ?

Question

Accepted Answer

Step:1 ：Find the volume of the solid generated by revolving the region bounded by the graph of (y=x^2), the vertical line (x=3), and the horizontal line (y=4) about the horizontal line (y=4) using the disk method. The radius of each disk is (4-x^2) and the area of each disk is (pi(4-x^2)^2). Integrate this area from (x=0) to (x=3).Step:2 ：Evaluate the integral to find the volume: (boxed{frac{123pi}{5}})

Answer

Step: 1 ：Find the volume of the solid generated by revolving the region bounded by the graph of (y=x^2), the vertical line (x=3), and the horizontal line (y=4) about the horizontal line (y=4) using the disk method. The radius of each disk is (4-x^2) and the area of each disk is (pi(4-x^2)^2). Integrate this area from (x=0) to (x=3).Step: 2 ：Evaluate the integral to find the volume: (boxed{frac{123pi}{5}})

What is the volume of the solid generated when the region bounded by the graph of $y=x^{2}$, the vertical line $x=3$, and the horizontal line $y=4$ is revolved about the horizontal line $y=4 ?$

Answer

Popular Problems