Question

Londyn and Landen are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 43.98 (about 14π ) cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?

Answer 1

Explanation:

The volume of a cone can be calculated as (1/3)πr^2h, so we can set that equal to 43.98:

(1/3)πr^2h = 43.98

Dividing both sides by (1/3)π:

r^2h = 43.98 * 3 / π

Solving for one of the variables in terms of the other requires choosing specific values for either radius or height. Here are two examples:

Example 1: Let's say r = 3.

Then

h = 43.98 * 3 / (π * 9) = 4.43

So one possible cone has height 4.43 and radius 3.

Example 2: Let's say h = 5.

Then

r^2 = 43.98 * 3 / (π * 5) = 25.51

So one possible cone has height 5 and radius 5.07.