Question

Noah and Lin are marketing paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 9 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?

if h=3, then r=


if r=2, then h=

Answer 1

Answer: r = 1.69 inches

h = 2.15 inches

Explanation: Volume of a solid is the amount of space contained within a solid.

Volume of a cone is directly proportional to radius and height:

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

They want the cones to hold the same volume of 9 cubic inches.

If height is 3:

`9=(1)/(3)\pi r^(2)3`

`\pi r^(2)=9`

`r^(2)=2.864`

r = 1.69 inches

When height is 3, radius is 1.69 inches for a cone to have 9 cubic inches of volume.

If radius is 2:

`9=(1)/(3)\pi (2)^(2)h`

`h=(9(3))/(4 \pi)`

h = 2.15 inches

If radius is 2 inches, height of the cone is 2.15 inches.