The dimensions of a cuboid are in the ratio 5 : 2 : 1. It's volume is 1250m³. Find the total surface area.

A cuboid is a three-dimensional analog of a rectangle in two dimensions.

Answer: The dimensions of a cuboid are in the ratio 5: 2:1. Its volume is 1250m³. The total surface area of the cuboid is 850 m².

Let's find the total surface area.

Explanation:

Let the dimensions of the cuboid be:

Length, l = 5x Breadth, b = 2x Height, h = 1x

Using these values, the volume of the cuboid would be:

V = l × b × h

V = (5x) × (2x) × (1x) = 1250

10x³ = 1250

x³ = 125

x = ³√125 = 5

Therefore, the dimensions are:

Length, l = 5x = 5 × 5 = 25m

Breadth, b = 2x = 2 × 5 = 10m

Height, h = 1x = 1 × 5 = 5m

Now the surface area of a cuboid is,

SA = 2(lb + bh + hl)

SA = 2(25 × 10 + 10 × 5 + 5 × 25)

SA = 2(250 + 50 + 125)

SA = 2 × 425

SA = 850 m²

Thus, the total surface area of the cuboid is 850 m².