# How do you determine the amount of liquid a paper cone can hold with a 1.5-inch diameter and a 5-inch height if the volume formula is given by Volume = (pi r^2 (h))/3 , where r= the radius , and h= the height of the cone?

May 30, 2018

$\approx 2.945$ cubic inches of liquid

#### Explanation:

We are given the volume of a cone is:

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

We are told that our cone has a diameter of 1.5 inches and a height of 5 inches.

Radius $\left(r\right) = \frac{1}{2} \times$ Diameter

$\therefore r = \frac{1.5}{2} = 0.75$ inches

Applying the formula above:

Volume $= \frac{1}{3} \times \pi \times {0.75}^{2} \times 5$

$\approx \frac{1}{3} \times 3.14159 \times 0.5625 \times 5$

$\approx 2.945$ cubic inches

Hence our cone can hold approximately 2.945 cubic inches of liquid.