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`

Step-by-step explanation

Step 1

the volume of a square pyramid is given by

`Volume=(side^2\cdot heigth)/(3)`

we are told that:

volume of the entire pyramid is

`\begin{gathered} 96cm^3=(side_1^2\cdot heigth_1)/(3) \\ 96cm^3=(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=(side^2\cdot heigth)/(3) \\ Volume=(3^2\cdot4)/(3)=3\cdot4=12 \\ Volume=12cm^3 \end{gathered}`

I hope this helps you