Question

A sphere is just enclosed inside a right circular cylinder. If the volume of the sphere is 20cm^3, find the volume of the gap between the cylinder and the sphere.

Answer 1

Answer:

30cm3

Step-by-step explanation:

There are three equations we need to know in this type of question - the volume of a cylinder, the

volume a sphere, and the remaining volume of the gap between the sphere and the cylinder.

Step 2

The volume of a cylinder of radius 'r' and height 'h' is πr

2h. Here, we know the sphere will fit in

exactly in the cylinder, so h=2r, and the formula now becomes 2πr

3

.

Step 3

The sphere will have the radius 'r' so its volume is

4

3

πr

3

.

Step 4

The volume of the gap between the cylinder and the sphere is all the volume inside the cylinder not

taken up by the sphere.

This is the difference between the volume of the cylinder and the volume of the sphere.

i.e. volume of the gap = 2πr

3

-

4

3

πr

3

Simplifying, volume of the gap =

2

3

πr

3

Step 5

So we have 3 equations:

Volume of the cylinder = 2πr

3

Volume of the sphere =

4

3

πr

3

Volume of the gap =

2

3

πr

3

Step 6

Here, we know that volume of the sphere is 20 cm3

. We need to find the volume of the cylinder.

Step 7

Substituting from the equation above, we get volume of the cylinder = 30 cm3