Question

A square pyramid has base edge length 10 cm. The slant height of the pyramid is 13 cm. What is the volume of the​ pyramid?

Answer 1

v=400 cm3

Explanation:

Answer 2

`V=400\ cm^(3)`

Explanation:

we know that

The volume of a pyramid is equal to

`V=(1)/(3)BH`

where

B is the area of the square base

H is the height of the pyramid

Find the area of the square base B

`B=b^(2)`

`b=10\ cm`

`B=10^(2)=100\ cm^(2)`

Find the height H of the pyramid

Applying the Pythagoras Theorem

`l^(2)=H^(2)+(b/2)^(2)`

we have

`b=10\ cm`

`l=13\ cm`

substitute

`13^(2)=H^(2)+(10/2)^(2)`

`169=H^(2)+25`

`H^(2)=169-25`

`H^(2)=144`

`H=12\ cm`

Find the volume

`V=(1)/(3)(100)(12)`

`V=400\ cm^(3)`