Question

A cone with a radius of 7ft and a height of 12ft is filled with wet sand. you took that sand and built a pyramid with a base of 4ft by 5ft how tall would the resulting pyramid be?

Answer 1

95.36 ft

Explanation:

Volume of a Cone
`=(1)/(3)\pi r^2 h`

Radius=7 ft, Height=12 ft

Therefore the volume of sand in the cone

`=(1)/(3)\pi *7^2*12\\=615.7522$ ft^2`

If the sand was used to build as pyramid with a base of 4ft by 5ft.

Volume of a Pyramid
`=(1)/(3)*$Base Area* Height`

`615.7522=(1)/(3)*(4*5)* Height\\615.7522=(20)/(3)* Height\\$Multiply both sides by (3)/(20)\\$Height =615.7522*(3)/(20)\\\\$Height of the pyramid=95.36 ft`