Question

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

Answer 1

The volume of the cone is

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

Given $V=9\pi.$ Then

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

$$r^2h=27$$

$r=3\ in, h=3\ in$

$$V=\dfrac{1}{3}\pi (3)^2 \cdot 3=9\pi(in^3)$$

$r=1\ in, h=27\ in$

$$V=\dfrac{1}{3}\pi (1)^2 \cdot 27=9\pi(in^3)$$

$r=2\ in, h=6.75\ in$

$$V=\dfrac{1}{3}\pi (2)^2 \cdot 6.75=9\pi(in^3)$$