# 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's the solution.

**Explanation:**

The x be the dimensions of the cuboid:

given the length (L) ,breadth (B) and height(H) are in the ration 5:2:1

Therefore,

L = 5x

B= 2x

H= 1x

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

V = Length × breadth × height

= (5x) × (2x) × (1x) = 1250m^{3}

==> 10x^{3} = 1250m^{3}

==> x^{3} = 125

==>x = 5

Therefore, the dimensions are:

L= 5x = 5 × 5 = 25m

B= 2x = 2 × 5 = 10m

H= 1x = 1 × 5 = 5m

TheTotal surface area of a cuboid = 2(lb + bh + hl)

= 2(25m × 10m + 10m × 5m + 5m × 25m)

= 2(250m^{2} + 50m^{2} + 125m^{2} )

= 2 × 425m^{2}

= 850 m^{2}

you could use this cuemath surface area of a cuboid calculator to verify the answer.