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

Answer:

$\large\boxed{V_{pyramid}=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism}}$

Step-by-step explanation:

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