Question

3.) The volume of a cylinder, V(h), is given by the area of the base times the height, h. The base of the cylinder shown below is 5 inches squared.

Part A: Write the function, V(h), that represents the volume of the cylinder.

Part B: Find V(3)

Part C: What does V(3) represent?

Answer 1

Explanation:

The volume of a cylinder is given by :

`V=\pi r^2 h` ...(1)

r is radius and h is height of the cylinder

The diameter of a cylinder = 5 inches

Radius = 5/2 = 2.5 inches

Part A :

Put r = 2.5 inch in equation (1)

`V=\pi (2.5)^2 h\\\\=6.25\pi h\ \text{inches}^3` .....(2)

Part B :

Put h = 3 in equation (2) as follows :

`V(3)=6.25\pi * 3\\\\=18.75\pi \text{inches}^3`

Part C:

V(3) represents the volume of the cylinder when its height is 3 inches.

Hence, this is the required solution.