Question

A company makes cones out of a solid foam. Each cone has a height of 9 inches, and it’s bade has a diameter of 5 inches. How much foam is needed to make 120 cones?

Answer 1

The volume of foam needed to make 120 cones, each with a 9-inch height and a 5-inch diameter base, is approximately 7,068.6 cubic inches.

Step-by-step explanation:

The question involves finding the volume of a single cone and then calculating the total volume of foam needed for producing 120 cones. To find the volume of one cone, we use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height. Given that the diameter of the base is 5 inches, the radius (r) would be half of that, which is 2.5 inches. The height (h) is given as 9 inches. Therefore, the volume of one cone is:

V = (1/3)π(2.5)²(9)

This simplifies to V ≈ 58.905 cubic inches (using 3.14159 for π). To find the volume for 120 cones, we multiply the volume of one cone by 120:

Total volume = 58.905 in³ × 120 ≈ 7,068.6 cubic inches.

This is the amount of foam needed to make 120 cones.

Answer 2

Step-by-step explanation:

The volume of a cone is given by the following equation:

`V = (πr^(2)h)/(3)`

where
`V` is the volume of the cone,
`r` is the radius of the base, and
`h` is the height of the cone.

In the given problem, we know that
`h = 9` and
`r = 2.5`. Using this, we can find the volume of a single cone:

`V = (π(2.5)^(2)(9))/(3)`

`V = (56.25π)/(3)`

`V = 18.75π`

Since the problem asks how much foam is needed to make 120 cones, we can multiply this result to get our answer:

`120 * 18.75π`

`2250π`