Question

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27 pi cm^3 cubed of melted purple liquid. The radius of the cone is 3 cm.

What is the height of the cone?
Either enter an exact answer in terms of pi or use 3.14 for pi.

Answer 1

9 cm

Explanation:

Use the cone volume formula, V =
`\pi`r²
`(h)/(3)`

Plug in the volume and radius, and solve for h, the height:

V =
`\pi`r²
`(h)/(3)`

27
`\pi` =
`\pi`(3²)
`(h)/(3)`

27
`\pi \\` = 9
`\pi`
`(h)/(3)`

3 =
`(h)/(3)`

9 = h

So, the height of the cone is 9 cm