SSC CHSL 2022 PYQ — Question 52

The correct answer is option 2 i.e. 177 cm²

Given:

l + b + h = 23

diagonal, d = $5\sqrt{7}$

Formula Used:

Diagonal of cuboid = $\sqrt{l^2 + b^2 + h^2}$

Surface area of cuboid = (lb + bh + hl)

Explanation:

According to the given question, l + b + h = 23

Squarying both sides, we get

⇒ (l + b + h)² = 529

⇒ l² + b² + h² + 2(lb + bh + hl) = 529

⇒ l² + b² + h² = 529 - 2(lb + bh + hl)   ....(i)

d = $\sqrt{l^2 + b^2 + h^2}$

⇒ $5\sqrt{7}$ = $\sqrt{l^2 + b^2 + h^2}$

Squarying both sides, we get

⇒ 175 = l² + b² + h² 

⇒ 175 = 529 - 2(lb + bh + hl) 

⇒ 2(lb + bh + hl) = 529 - 175

⇒ lb + bh + hl = 177

HEnce the surface area of cube is 177 cm².