Question

// The length of the diagonal of a cuboid be 4√3 cm ...

If the sum of the edges
of the cuboid be 48 cm, then find the total surface area of it..



I will mark the right answer as brainliest.... ​

Answer 1

Answer:

Total surface area = 96 cm²

Step-by-step explanation:

Length of diagonal of cuboid = √(l² + b² + h²)

Length of diagonal of cuboid = √(l² + b² + h²)Sum of edges of cuboid = 4(l + b + h)

Length of diagonal of cuboid = √(l² + b² + h²)Sum of edges of cuboid = 4(l + b + h) Total surface area of cuboid = 2(lb + bh + hl)

Length of diagonal of cuboid = 4√3 cm

4√3 = √(l² + b² + h²)

Squaring both sides,

(4√3)² = l² + b² + h²

l² + b² + h² = 16 × 3 = 48

Sum of edges of cuboid = 48 cm

48 = 4(l + b + h)

12 = (l + b + h)

Squaring both sides,

144 = (l + b + h)²

144 = l² + b² + h² + 2(lb + bh + hl)

We have the value of l² + b² + c²,

144 = 48 + 2(lb + bh + hl)

2(lb + bh + hl) = 144 - 48 = 96

LHS is the formula of total surface area.

Therefore, total surface area = 96 cm²