Question

Kennedy’s Ice Cream Shoppe is looking at two different containers in which to serve the triple Play — three scoops of ice cream. One container is a cylinder and the other is a cone as shown. All ice cream scoops have a diameter of 3 inches.

Kennedy wants to use the container with the least wasted space. Which container should the ice cream shoppe use? Use 3.14 for pi.p

Answer 1

The answer is letter C

Answer 2

Kennedy's Ice Cream Shoppe should use the cone-shaped container, as it results in less wasted space when serving three scoops of ice cream with a diameter of 3 inches.

Let's start by calculating the volumes of the two containers: the cone and the cylinder. The container with the smaller volume will result in less wasted space when serving three scoops of ice cream with a diameter of 3 inches.

For the cone:

Given:

Diameter of the cone's base = 6.5 inches

Height of the cone = 6.5 inches

The formula for the volume V of a cone is
`\(V = (1)/(3) \pi r^2 h\)`, where r is the radius of the base and h is the height.

First, let's find the radius of the cone's base:

Radius
`\(r = (6.5)/(2) = 3.25\)` inches

Now, let's calculate the volume of the cone:

`\[V_{\text{cone}} = (1)/(3) * 3.14 * 3.25^2 * 6.5\]`

For the cylinder:

Given:

Diameter of the cylinder = 4 inches

Height of the cylinder = 9 inches

The formula for the volume V of a cylinder is
`\(V = \pi r^2 h\)`, where r is the radius of the base and h is the height.

First, let's find the radius of the cylinder:

Radius
`\(r = (4)/(2) = 2\)` inches

Now, let's calculate the volume of the cylinder:

`\[V_{\text{cylinder}} = 3.14 * 2^2 * 9\]`

Let's compare the volumes of the two containers to determine which one has less wasted space when serving three scoops of ice cream.

For the cone:

`\[V_{\text{cone}} = (1)/(3) * 3.14 * 3.25^2 * 6.5\]`

`\[V_{\text{cone}} \approx 70.22 \text{ cubic inches}\]`

For the cylinder:

`\[V_{\text{cylinder}} = 3.14 * 2^2 * 9\]`

`\[V_{\text{cylinder}} = 3.14 * 4 * 9\]`

`\[V_{\text{cylinder}} = 113.04 \text{ cubic inches}\]`

Comparing the volumes:

The cone's volume is approximately 70.22 cubic inches, while the cylinder's volume is 113.04 cubic inches.

Therefore, the cone would result in less wasted space when serving three scoops of ice cream with a diameter of 3 inches. Kennedy's Ice Cream Shoppe should use the cone-shaped container.