The dimensions of a cuboid are in the ratio 5:2:1. Its volume is 1250 cubic meters. Find the total surface area of the cuboid.

A cuboid is a three-dimensional figure.

Answer: If the dimensions of a cuboid are in the ratio 5:2:1 and its volume is 1250 cubic meters, the total surface area of the cuboid is 850 sq.m.

Here is the solution.

Explanation:

Given, length (L), breadth (B) and height(H) are in the ratio of 5:2:1.

So, let us assume that,

L = 5x

B= 2x

H= 1x

We know that volume of a cuboid is the product of its length, breadth, and height.

Volume = length × breadth × height

(5x) × (2x) × (1x) = 1250m³

⇒ 10x³ = 1250m³

⇒ x³ = 125

⇒ x = 5

Therefore, the dimensions are:

L= 5x = 5 × 5 = 25 m

B= 2x = 2 × 5 = 10 m

H= 1x = 1 × 5 = 5 m

We know that the total surface area of a cuboid = 2(lb + bh + hl) square units.

⇒ 2(25m × 10m + 10m × 5m + 5m × 25m)

⇒ 2 (250 m² + 50 m² + 125 m² )

⇒ 2 × 425m²

= 850 m²

You could use this Cuemath's surface area of a cuboid calculator to verify the answer.

Thus, if the dimensions of a cuboid are in the ratio 5:2:1 and its volume is 1250 cubic meters, the total surface area of the cuboid is 850 sq.m.