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

Answer:

95.36 ft

Step-by-step explanation:

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

Radius=7 ft, Height=12 ft

Therefore the volume of sand in the cone

$=\frac{1}{3}\pi *7^2*12\\=615.7522 ft^2$

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

Volume of a Pyramid$=\frac{1}{3}* Base Area* Height$

$615.7522=\frac{1}{3}*(4*5)* Height\\615.7522=\dfrac{20}{3}* Height\\ Multiply both sides by \dfrac{3}{20}\\ Height =615.7522*\dfrac{3}{20}\\\\ Height of the pyramid=95.36 ft$