Solve the problem.
-For what value of $b$ is the volume of the ellipsoid $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { 81 } = 1$ equal to $9 \pi$ ?
A) $b = \frac { 3 } { 10 }$
B) $b = \frac { 1 } { 10 }$
C) $b = \frac { 3 } { 20 }$
D) $b = \frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

The volume of an ellipsoid is given by $ V = \frac{4}{3} \pi a b c $. Here, $ a = 5 $, $ c = 9 $, and $ b $ is unknown. Setting the volume equal to $ 9 \pi $, we solve $ \frac{4}{3} \pi \times 5 \times b \times 9 = 9 \pi $, leading to $ b = \frac{3}{20} $.

Solve the Problem bbb Is the Volume of the Ellipsoid x225+y2b2+z281=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { 81 } = 125x2​+b2y2​+81z2​=1

Solve the Problem $b$ Is the Volume of the Ellipsoid $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { 81 } = 1$