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

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 $9 \ cm$

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,  

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

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

$27 \pi=\frac{1}{3} \pi(3)^{2} h$

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 $9 \ cm$