Question

If the height and the slant height of a square pyramid are $8cm$ and $10cm$ respectively, what is the volume of the pyramid?

• A. $192cubiccentimetres$
• B. $384cubiccentimetres$
• C. $120cubiccentimetres$
  
• D. $96cubiccentimetres$
  

Answer 1

The correct option is B $384cubiccentimetres$

Note first that the Volume of a square pyramid = $\frac{1}{3}\times Basearea\times Height$
Given that the height and the slant height of a square pyramid are $8cm$ and $10cm$ respectively.
We have$Halfthebaseedge=\sqrt{(Slantheightofthepyramid{)}^2-(Heightofthesquarepyramid{)}^2}=\sqrt{{100}^2-8^2}=\sqrt{100-64}=\sqrt{36}=6cm$
$\therefore Baseedge=12cmandthebasearea=144c{m}^2$
Thus, the required volume = $\frac{1}{3}\times 144\times 8=384cubiccentimetres$