Question

What is the exact volume of the cylinder?

• A. $18\mathrm{\pi }{\text{in}}^3$
• B. $36\mathrm{\pi }{\text{in}}^3$
• C. $54\mathrm{\pi }{\text{in}}^3$
• D. $63\mathrm{\pi }{\text{in}}^3$

Answer 1

The correct option is C

$54\mathrm{\pi }{\text{in}}^3$

Explanation for the correct option.

Finding the volume of the cylinder.

The volume of the cylinder is the space occupied by the cylinder. It is given as,

$V=\mathrm{\pi }{r}^{2}h$

As we can see in the image that the radius of the cylinder is $3\mathrm{in}$ while the height of the cylinder is $6\mathrm{in}$, therefore, the volume of the cylinder can be written as,

$\begin{array}{rcl}V& =& \mathrm{\pi }{r}^{2}h\\ & \Rightarrow & V=\mathrm{\pi }\times {\left(3\right)}^2\times 6\\ & \Rightarrow & \mathrm{V}=\mathrm{\pi }\times 9\times 6\\ & \Rightarrow & \mathrm{V}=54\mathrm{\pi }\end{array}$

Hence, the volume of the cylinder with a radius of $3\mathrm{in}$ and height of $6\mathrm{in}$ is $54\mathrm{\pi }{\text{in}}^3$.

Therefore, the correct answer is option (C).