Question

The volume of a cylinder is 40 f3. Which expression represents the volume of a cone with the same base and height as

the cylinder?
O 3(40) ft
O
1
40
O (40) At
o 3 (402)

Answer 1

Option (3)

Explanation:

Volume of the cylinder = 40 ft³

Since, volume of a cylinder is given by the expression,

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

Here, r = radius of the circular base

h = Height of the cylinder

40 =
`\pi r^(2)h`

`h=(40)/(\pi r^2)` ------(1)

Volume of a cone =
`(1)/(3)\pi r^(2) h`

By substituting the value of 'h' from equation (1)

Volume of the cone =
`(1)/(3)\pi r^(2)((40)/(\pi r^(2) ) )`

=
`(1)/(3)(40)` ft³

Therefore, Option (3) will be the correct option.