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

Answer:

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

Step-by-step 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

$V_c=\frac{1}{3} Bh$ ----> 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

$V_c=\frac{1}{3} V_p$

solve for V_p

$V_p=3V_c$

therefore

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