Question

What is total surface area of cuboid if the diagonal of a cuboid is 5√5 cm and sum of all edges of a cuboid is 76 cm? 
1. 236 cm²
2. 256 cm2
3. 180 cm2
4. 196 cm2

Answer 1

Correct Answer - Option 1 : 236 cm²

Given:

Sum of all edges of a cuboid is 76 cm.

Diagonal of a cuboid is 5√5 cm. 

Formula Used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Total Surface Area of a Cuboid = 2(lb + bh + hl)

Diagonal of a cuboid = √(l² + b² + h²) 

Calculation:

Diagonal of a cuboid is 5√5 cm.

D =√(l2 + b2 + h2)

⇒ (5√5)² = l2 + b2 + h2

⇒ l2 + b2 + h2 = 125      ----(I)

Sum of all edges of a cuboid is 76 cm.

⇒ 4(l +b + h) = 76 cm

⇒ (l + b + h) = 19 cm

Squaring on both sides,

⇒ (l + b + h)2 = 19²  

⇒ l2 + b2 + h2 + 2(lb + bh + hl) = 361

⇒ 2(lb + bh + hl) = 361 – ( l2 + b2 + h2)

⇒ 2(lb + bh + hl) = 361 – 125

⇒ 2(lb + bh + hl) = 236

∴ Total surface area of cuboid is 236 cm².