Find the volume of the described solid.
-The base of the solid is the disk $x ^ { 2 } + y ^ { 2 } \leq 9$. The cross sections by planes perpendicular to the $y$-axis between $y = - 3$ and $y = 3$ are isosceles right triangles with one leg in the disk.
A) 90
B) 18
C) 72
D) 144

Question

Quizplus · Accepted Answer

The area of the base is $9\pi$. The height of each cross section is $6 - |y|$. So the volume is$$V = \int_{-3}^3 \frac{1}{2} (6 - |y|) (9\pi) \ dy = 72\pi$$

Find the Volume of the Described Solid x2+y2≤9x ^ { 2 } + y ^ { 2 } \leq 9x2+y2≤9

Find the Volume of the Described Solid $x ^ { 2 } + y ^ { 2 } \leq 9$