Question

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 has a diameter of 5 inches.

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

Part B: find V(3) and tell what it represents

Answer 1

Part a)
`V(h)=6.25\pi h\ in^3`

Part b)
`V(3)=18.75\pi\ in^3` (see the explanation)

Explanation:

we know that

The volume of a cylinder is equal to

`V=Bh`

where

B is the area of the base of cylinder

h is the height of the cylinder

we have that

`B=\pi r^(2)`

Part a) Write the function, V(h), that represents the volume of the cylinder

we have

`r=5/2=2.5\ in` ----> the radius is half the diameter

substitute

`B=\pi (2.5)^(2)`

`B=6.25\pi\ in^2`

The volume is

`V(h)=6.25\pi h\ in^3`

Part b) Find V(3) and tell what it represents

V(3) represent the volume of the cylinder with a height of 3 inches

so

For h=3 in

substitute

`V(3)=6.25\pi(3)\ in^3`

`V(3)=18.75\pi\ in^3`