SSC CPO 2023 PYQ — Question 141

The correct answer is option 4. i.e. 960 cm ³

Given that

A right square pyramid having a lateral surface area is 624 cm²

The length of the diagonal of the square is $24\;{ \sqrt 2}$ cm

Volume of a pyramid = $1 \over 3$ × (Base Area) × (Height)

Lateral surface area = 2 × base × slant height (l)

Diagonal of pyramid = side$\sqrt{2}$

⇒  side$\sqrt{2}$ = $24\;{ \sqrt 2}$

side of pyramid (a) = 24 cm

⇒ 2 × base × slant height = 624

⇒ slant height = $624 \over (2 \times 24)$ = 13 cm

⇒ Height  = √(l² - $({a \over 2})^2$) = √(13² - $({24 \over 2})^2$) = √ (169 - 144) = √25 = 5 cm

Hence, Volume of a pyramid = $1 \over 3$ × 24² × 5 = 960 cm³