Question

Drag and drop the answers into the boxes to complete this informal argument explaining how to derive the formula for the volume of a cone.

Since the volume of a cone is part of the volume of a cylinder with the same base and height, find the volume of a cylinder first. The base of a cylinder is a circle. The area of the base of a cylinder is _______ , where r represents the radius. The volume of a cylinder can be described as slices of the base stacked upon each other. So, the volume of the cylinder can be found by multiplying the area of the circle by the height h of the cylinder. The volume of a cone is ______ of the volume of a cylinder. Therefore, the formula for the volume of a cone is _______.

1/3
1/2
1/3πr^2h
1/2πr^2h
πr^2h
πr^2

Answer 1

First blank =
`\pi r^(2)`

Second blank =
`(1)/(3)`

Third blank =
`(1)/(3) \pi r^(2) h`

Explanation:

We are given,

The argument to explain the derivation of the formula for the volume of a cone.

According to the explanation, we have,

First blank: It represents the area of the base of the cylinder.

Since, the base of the cylinder is a circle.

And, area of the circle =
`\pi r^(2)`

Thus, the first blank =
`\pi r^(2)`

Second blank: It represents the number by which volume of the cylinder is multiplied to obtain the volume of the cone.

Since, we know,

`(1)/(3)` of Volume of cylinder is given by volume of the cone.

Hence, the second blank =
`(1)/(3)`

Third blank: It represents the formula for the volume of the cone.

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

Thus, third blank =
`(1)/(3) \pi r^(2) h`