Question

a prism and a pyramid are side by side. they have the same height and same base are. the volume of the prism would be ? times the volume of the pyramid?

Answer 1

The volume of the prism is 3 times the volume of the cone

Explanation:

step 1

we know that

The area of the prism is given by the formula

`V_p=Bh` ----> equation A

where

B is the area of the circular base

h is the height of the prism

step 2

The area of the cone is given by the formula

`V_c=(1)/(3) Bh` ----> equation B

where

B is the area of the circular base

h is the height of the cone

In this problem we have that they have the same height and same base area

so

substitute equation A in equation B

`V_c=(1)/(3) V_p`

solve for V_p

`V_p=3V_c`

therefore

The volume of the prism is 3 times the volume of the cone