Question

a) A triangle pyramid has a base area of 72 cm squared and a height/altitude of 9 cm. If a cross section is cut 3 cm from the base of the pyramid, find the area of the cross section.b) Find the volume of the entire pyramid.

Answer 1

Given that a triangle pyramid has a base area of 72 cm squared and a height/altitude of 9 cm.

A cross-section is cut 3 cm from the base of the pyramid.

So, the dilating factor is

`(1)/(3)`

Now, the base area of the triangle pyramid is 72 square sm.

So, the area of the cross-section is

`\begin{gathered} A=((1)/(3))^2*72 \\ =(1)/(9)*72 \\ =8 \end{gathered}`

So, the area of the cross-section is 8 square cm

Now, the given height of the pyramid is 9 cm.

So, the volume of the entire pyramid is

`\begin{gathered} V=(1)/(3)Ah \\ =(1)/(3)*72*9 \\ =216 \end{gathered}`

Hence, the volume of the entire pyramid is 216 cubic centimeters.