Question

Aran moved a cone-shaped pile of sand that had a height of 4 ft and a radius of 3.2 ft. He used all of the sand to fill a cylindrical pit with a radius of 6 ft.

How high did the sand reach in the pit? Use 3.14 to approximate pi and round your answer to one decimal place.


ft


I understand the first part I just need help with the second part. The first is 42.87(V=cone) I need help finding the height of the cylinder.

Answer 1

so first find the volume of the cone
1/3 times height times area of base
area of bse=circle=pi times radius^2
pi aprox 3.141592
radius=3.2
3.141592 times 3.2^2=32.1699
1/3 times 4 times 32.1699=42.89

volume=42.89

volume of cylinder filled=area of base times height
area of base=circle
radius=6
3.141592 times 6^2=113.097
113.097 times h=42.89
divide both sdies by 113.097
height=0.379 ft or aprox 0.4 ft

Answer 2

Since the cone filled the entire hole, that must be the volume of the cylinder too.

V = pi * r^2 * h

42.87 = 3.14 * 6^2 * h

42.87 = 113.04h

Divide 113.04 to both sides:

h = 0.379246285

So the height is approximately 0.4 feet.