Answer:
The volume of the cylinder is
![112\pi\ cm^(3)](https://img.qammunity.org/2020/formulas/mathematics/college/1f7h47wvc08uhq2plgn7khaxs5i57pl5n1.png)
Explanation:
we know that
The volume of the cylinder is equal to
![V=Bh](https://img.qammunity.org/2020/formulas/mathematics/college/1z8biyc5dxidzjd7gaahhzli35rckolci0.png)
where
B is the area of the base
h is the height of the prism
![B=\pi r^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/d40zimbod8mq5og0siygmjje9tcv6xu7y3.png)
In this problem we have
![r=4\ cm](https://img.qammunity.org/2020/formulas/mathematics/high-school/i20ehdj1t52e3oo2213a2sovqqvp9qscgu.png)
![h=7\ cm](https://img.qammunity.org/2020/formulas/mathematics/college/kl1jqfkjo75qp2nklmgriavkl0qq2vmsu3.png)
substitute
Find the area of the base B
![B=\pi (4^(2))](https://img.qammunity.org/2020/formulas/mathematics/college/tmdoigri6zgw4jjktjrhtheyeh2uwpby2o.png)
![B=16\pi\ cm^(2)](https://img.qammunity.org/2020/formulas/mathematics/college/5wexk6amwi00axi913h8awof5i9est2kro.png)
substitute in the formula of the volume
![V=16\pi (7)](https://img.qammunity.org/2020/formulas/mathematics/college/b5avzonu8re5sforqzzeo4aq0ozdl5rcgv.png)
![V=112\pi\ cm^(3)](https://img.qammunity.org/2020/formulas/mathematics/college/k3kmk7maemgpt4lspffhrp7oodx5c45sop.png)