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\pi27π27, pi cm^3

3

cubed of melted purple liquid. The radius of the cone is 333 cm.

Answer 1

9 cm

Step-by-step explanation:

I did it on khan

Answer 2

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\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?

Answer:

The height of the cone is
`9 \ cm`

Step-by-step explanation:

It is given that the radius of the cone is
`3 \ cm`

The volume of the cone is
`27\pi`

The height of the cone can be determine using the formula,

`$V=(1)/(3) \pi r^(2) h$`

Substituting the values
`V=27 \pi` and
`r=3`, we get,

`$27 \pi=(1)/(3) \pi(3)^(2) h$`

Multiplying both sides by 3, we have,

`$81 \pi= 9\pi h$`

Dividing both sides by
`$9 \pi$`, we have,

`9=h`

Thus, the height of the cone is
`9 \ cm`