Question

The diagram below shows a right square pyramid with a base that is 6 centimeters (cm) on each sideand a height of 8 cm. The pyramid is intersected by a plane exactly halfway between the top andbottom. The intersection of the plane and the pyramid creates a smaller, similar pyramid as shown inthe shaded area. If the volume of the entire pyramid is 96 cm2, what is the volume of the smallerpyramid?Scale Factor = 5O 36 cm24 cm54 cm12 cm

Answer 1

$12cm^3$

Explanation

Step 1

the volume of a square pyramid is given by

$Volume=\frac{side^2\cdot heigth}{3}$

we are told that:

volume of the entire pyramid is

$\begin{gathered} 96cm^3=\frac{side_1^2\cdot heigth_1}{3} \\ 96cm^3=\frac{6^2\cdot8}{3} \\ 96cm^3=96cm^3 \end{gathered}$

Step 2

now, the measures are reducted by a scale factor of 0.5,it means.

$\begin{gathered} \text{side}_2=0.5\cdot side_1=0.5\cdot6=3 \\ \text{height}_2=0.5\cdot height_1=0.5\cdot8=4 \end{gathered}$

now, replace

the volume of the small pyramid would be.

$\begin{gathered} Volume=\frac{side^2\cdot heigth}{3} \\ Volume=\frac{3^2\cdot4}{3}=3\cdot4=12 \\ Volume=12cm^3 \end{gathered}$

I hope this helps you