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

Step-by-step 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:

$V=\frac{1}{3}\pi r^{2}h$

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

If height is 3:

$9=\frac{1}{3}\pi r^{2}3$

$\pi r^{2}=9$

$r^{2}=2.864$

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:

$9=\frac{1}{3}\pi (2)^{2}h$

$h=\frac{9(3)}{4 \pi}$

h = 2.15 inches

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