Question

A figure is a cylinder with a radius of 6 inches and a height of 10 inches. On top of the cylinder is a hemisphere with a radius of 6 inches. Find the volume.
A) 102π in3
B) 348π in3
C) 504π in3
D) 888π in3

Answer 1

C, 504$\pi$ in3

Answer 2

Answer:

C. $504\pi\text{ inches}^3$

Step-by-step explanation:

We have been given that a figure is a cylinder with a radius of 6 inches and a height of 10 inches. On top of the cylinder is a hemisphere with a radius of 6 inches.

The volume of our given figure will be equal to volume of cylinder plus volume of hemisphere.

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

r = Radius of cylinder,

h = height cylinder.

Upon substituting our given values in above formula we will get,

$\text{Volume of cylinder}=\pi\text{(6 inch)}^2*\text{ 10 inches}$

$\text{Volume of cylinder}=\pi*36\text{ inch}^2*\text{ 10 inches}$

$\text{Volume of cylinder}=360\pi\text{ inch}3$

Now let us find the volume oh hemisphere part of our figure using formula,

$\text{Volume of hemisphere}=\frac{2}{3}\pi r^3$

$\text{Volume of hemisphere}=\frac{2}{3}\pi*\text{ 6 inches}^3$

$\text{Volume of hemisphere}=\frac{2}{3}\pi*216\text{ inches}^3$

$\text{Volume of hemisphere}=\pi*2*72\text{ inches}^3$

$\text{Volume of hemisphere}=144\pi\text{ inches}^3$

$\text{Volume of the figure}=\text{Volume of cylinder + Volume of hemisphere}$

$\text{Volume of the figure}=360\pi\text{ inch}3+144\pi\text{ inches}^3$

$\text{Volume of the figure}=504\pi\text{ inches}^3$

Therefore, the volume of our given figure is $504\pi\text{ inches}^3$ and option C is the correct choice.