Find the volume of the described solid.
-The solid lies between planes perpendicular to the $x$-axis at $x = - 6$ and $x = 6$. The cross sections perpendicular to the $x$-axis between these planes are squares whose bases run from the semicircle $y = - \sqrt { 36 - x ^ { 2 } }$ to the semicircle $y = \sqrt { 36 - x ^ { 2 } }$.
A) 144
B) 1152
C) 288
D) 576

Question

Quizplus · Accepted Answer

The area of a cross section is $$A(x) = 2\sqrt { 36 - x ^ { 2 } } \cdot 2\sqrt { 36 - x ^ { 2 } } = 4(36 - x ^ { 2 } ) = 144 - 4x ^ { 2 }$$So, the volume of the solid is$$V = \int_{-6}^6 (144 - 4x ^ { 2 } ) \ dx = \left[ 144x - \frac { 4x ^ { 3 } } { 3 } \right]_{-6}^6 = 1152$$

Find the Volume of the Described Solid xxx -Axis At x=−6x = - 6x=−6

Find the Volume of the Described Solid $x$ -Axis At $x = - 6$