Question

The slant height of a square pyramid is 10 cm and its surface area is 144 square centimetres. What is the volume of the square pyramid?

• A. $384cubiccentimetres$
• B. $400cubiccentimetres$
• C. $192cubiccentimetres$
• D. $100cubiccentimetres$

Answer 1

The correct option is A $384cubiccentimetres$

Note first that the Volume of a square pyramid = $\frac{1}{3}\times Basearea\times Height$
Given that the base area of the square pyramid = 144cm and the slant height of a square pyramid is 10 cm
$⟹Baseedge=\sqrt{144}=12cm$
Now, $Heightofthesquarepyramid=\sqrt{(Slantheightofthepyramid{)}^2-(Halfthebaseedge{)}^2}=\sqrt{{100}^2-6^2}=\sqrt{100-36}=\sqrt{64}=8cm$
Thus, the required volume = $\frac{1}{3}\times 144\times 8=384cubiccentimetres$