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

Answer:

$V=400\ cm^{3}$

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

$V=\frac{1}{3}BH$

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

$V=\frac{1}{3}(100)(12)$

$V=400\ cm^{3}$

Answer 2

Answer:

v=400 cm3

Step-by-step explanation: