Question

Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 97 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?​

Answer 1

`r = 5` --- Radius

`h = 3.9` --- Height

Explanation:

Given

Shape: Cone

`Volume = 97in^3`

Required

Determine different possible values of radius and height

The volume (V) of a cone is calculated as:

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

Substitute 97 for V

`97 = (1)/(3)\pi r^2h`

Multiply both sides by 3

`3 * 97 = (1)/(3)\pi r^2h*3`

`291 = \pi r^2h`

Take
`\pi` as 3.14

`291 = 3.14* r^2h`

Divide both sides by 3.14

`(291)/(3.14) = (3.14* r^2h)/(3.14)`

`(291)/(3.14) = r^2h`

`92.68 = r^2h`

From the question, we understand that:

`r \\e h`

So, we have to assume a value for either r or h and then solve for the other variable.

Let
`r = 5`

So, We have:

`96.28 = 5^2 * h`

`96.28 = 25 * h`

Make h the subject

`h = (96.28)/(25)`

`h = 3.8512`

`h = 3.9` --- approximated

Note that there are other different possible values of h that is true for

`92.68 = r^2h` where
`r \\e h`