Answer to Question #163426 in Math for Mr

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

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

$r^2h=27$

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

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

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

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

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

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