Question

A snack bar sells popcorn in cone-shaped containers. One container has a diameter of 8 inches and a height of 10 inches. How many cubic inches of popcorn does 3 containers hold?Round to the nearest tenth.

Answer 1

The three containers can contain 502.4 cubic inches of popcorn

Explanation:

Given

Cone Shaped Containers

Diameter = 8 inches

Height = 10 inches

Required

Number of cubic inches of popcorn 3 containers hold.

The size of a shape is measured in cubic units and is represented by the volume of that shape.

This means that the interpretation of this question is to calculate the volume of the cone shaped containers.

Given that the container are cone shaped and assuming that each container are of the same size

The volume of a cone is calculated using

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

Where

V represents volume of the cone

r represents radius of the cone

h represents radius of the cone

First, the radius of the cone needs to be calculated

Radius is calculated by half of diameter.

Mathematically,

`r = (1)/(2)d`

where d represents diameter of the cone

So,
`r = (1)/(2) * 8`

`r = 4 inches`

Hence,
`V = (1)/(3)\pi r^2h` becomes

`V = (1)/(3)\pi * 4^2 * 10`

`V = (1)/(3)\pi * 16 * 10`

`V = (1)/(3)\pi * 160`

`V = (160)/(3)\pi`

If the volume of 1 container is
`(160)/(3)\pi`, the volume of 3 containers will be 3 multiplied by
`(160)/(3)\pi`

Let the volume of 3 containers be represented by
`V_3`

`V_3 = 3 * (160)/(3)\pi`

`V_3 = 160\pi`

Taking π as 3.14

`V_3 = 160 * 3.14`

`V_3 = 502.4`

Hence, the three containers can contain 502.4 cubic inches of popcorn