Find the volume of the solid whose base is the circle x^2 + y^2 = 81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Find the area of the vertical cross section at the level x=7
Find volume.

Question

Find the volume of the solid whose base is the circle x^2 + y^2 = 81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Find the area of the vertical cross section  at the level x=7
Find volume.

kainui · Answer

First off, where are you running into trouble? You can help yourself out a tremendous amount by simply drawing it out on a graph with axes labeled.

dumbcow · Answer

|dw:1329555309262:dw|
$$V = \int\limits_{-9}^{9}A(x) dx$$
due to symmetry we can set the limits from 0 to 9, and double the integral
$$V = 4\int\limits_{0}^{9}(81-x^{2}) dx$$
$$= 4 | 81x - x^{3}/3$$
$$= 4(81(9) -9^{3}/3)$$
$$= 2880$$