Answer to Question #163426 in Math for Mr

Question #163426

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 for the cones?


1
Expert's answer
2021-02-24T06:50:42-0500

The volume of the cone is


V=13πr2hV=\dfrac{1}{3}\pi r^2 h

Given V=9π.V=9\pi. Then


13πr2h=9π\dfrac{1}{3}\pi r^2 h =9\pi

r2h=27r^2h=27

r=3 in,h=3 inr=3\ in, h=3\ in


V=13π(3)23=9π(in3)V=\dfrac{1}{3}\pi (3)^2 \cdot 3=9\pi(in^3)

r=1 in,h=27 inr=1\ in, h=27\ in


V=13π(1)227=9π(in3)V=\dfrac{1}{3}\pi (1)^2 \cdot 27=9\pi(in^3)

r=2 in,h=6.75 inr=2\ in, h=6.75\ in


V=13π(2)26.75=9π(in3)V=\dfrac{1}{3}\pi (2)^2 \cdot 6.75=9\pi(in^3)


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