Question

Suppose that a sphere with radius 5a has the same volume as a cylinder of radius 2a What is the height of the cylinder? Give your answer in terms of a. Use the formulas V= 4/pi r^3 and V=pi(r)^2h for the volumes of a sphere and cylinder respectively.

Answer 1

Answer: $h = \frac{125a}{3}$

Step-by-step explanation:

Volume of sphere = $\frac{4}{3}\pi r^{3}$

radius = $5a$

Volume of cylinder = $\pi r^{2}h$

radius = $2a$

substituting the radius given and equating the two , we have :

$\frac{4}{3}\pi (5a)^{3} = \pi (a)^{2}h$

$\pi$ is common to the two , this means that it cancels out , the equation then becomes :

$\frac{4}{3}(125a^{3}) = 4a^{2}h$

$a^{2}$ is also common , then we have

$\frac{4}{3}(125a) = 4h$

multiply through by 3

$4(125a) = 12h$

divide through by 4

$125a = 3h$

divide through by 3

$h = \frac{125a}{3}$