Question

A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h,of the prism. Which expression gives the volume of the pyramid

Answer 1

V = 1/6 BH

Explanation:

the volume of a pyramid is 1/3 BH , since the pyramid is only half the height of the prism you'll have to multiply 1/3 x 2 = 1/6

Answer 2

`\large\boxed{V_(pyramid)=(1)/(6)Bh=(1)/(6)V_(prism)}`

Explanation:

`B-\text{base area}\\h-\text{height of the prism}\\(1)/(2)h-\text{height of the pyramid}\\\\\text{The formula of a volume of a prism:}\\\\V_(prism)=Bh\\\\\text{The formula of a volume of a pyramid:}\\\\V_(pyramid)=(1)/(3)Bh\to V_(pyramid)=(1)/(3)B\left((1)/(2)h\right)=(1)/(6)Bh=(1)/(6)V_{prism{`