Question

What is the total volume of snow used to make the snowman if the head is 12 inches wide, the middle is 16 inches wide,and the bottom is 18 inches wide

Answer 1

726.65 cubic inches

Explanation:

We are going to assume that the head, middle and bottom are spheres.

The formula to get the volume of a sphere is

`V= (4)/(3)\pi r^(2)` where r is the radius of the sphere.

Now, let's proceed to apply this formula to the 3 spheres of the snowman:

The head is 12 inches wide (diameter), thus, the radius would be 6 inches:

`V= (4)/(3)\pi r^(2)\\V= (4)/(3)\pi 6^(2)\\V= (4)/(3)\pi 36\\V=(144\pi )/(3) \\V=38\pi` cubic inches

The middle is 16 inches wide (diameter), thus, the radius would be 8 inches.

`V= (4)/(3)\pi r^(2)\\V= (4)/(3)\pi 8^(2)\\V= (4)/(3)\pi 64\\V=(256\pi )/(3) \\V=85.3\pi` cubic inches

The bottom is 18 inches wide (diameter), thus the radius would be 9 inches.

`V= (4)/(3)\pi r^(2)\\V= (4)/(3)\pi 9^(2)\\V= (4)/(3)\pi 81\\V=(324\pi )/(3) \\V=108\pi` cubic inches.

Now, to get the total volume of the snowman we're going to sum up the volume of all three spheres:

Total volume =
`38\pi +85.3\pi +108\pi =231.3\pi` cubic inches.

If we take pi = 3.1416,

Total volume =
`231.3(3.1416)=726.65` cubic inches.