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

Answer:

The volume of the cylinder B is 251.2 cubic inches.    

Step-by-step 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,

$254.34=k\times3^2\times 9$

$254.34=k\times81$

$k=\frac{254.34}{81}$

$k=3.14$

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

$V=3.14r^2h$

$V=3.14\times 4^2\times 5$

$V=3.14\times 16\times 5$

$V=251.2in^3$

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