Question

The volume of a cylinder varies jointly with the square of its radius and with its height: Cylinder A has a volume of 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches. What is the volume of cylinder B, which has a radius of 4 inches and a height of 5 inches?

Answer 1

The volume of the cylinder B is 251.2 cubic inches.

Explanation:

Given : The volume of a cylinder varies jointly with the square of its radius and with its height: Cylinder A has a volume of 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches.

To find : What is the volume of cylinder B, which has a radius of 4 inches and a height of 5 inches?

Solution :

The volume of a cylinder varies jointly with the square of its radius and with its height i.e. the volume is

`V=k r^2h`

Where, k varies jointly

Now, Cylinder A has a volume of 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches

i.e. V=254.34 cubic inches , r=3 inches and h=9 inches

Substitute values in the formula,

`254.34=k*3^2* 9`

`254.34=k*81`

`k=(254.34)/(81)`

`k=3.14`

Now, The volume of cylinder B, which has a radius of 4 inches and a height of 5 inches is given by,

`V=3.14r^2h`

`V=3.14* 4^2* 5`

`V=3.14* 16* 5`

`V=251.2in^3`

Therefore, The volume of the cylinder B is 251.2 cubic inches.