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.
The x be the dimensions of the cuboid:
given the length (L) ,breadth (B) and height(H) are in the ration 5:2:1
L = 5x
We know that Volume of a cuboid is the product of its length breadth and height.
V = Length × breadth × height
= (5x) × (2x) × (1x) = 1250m3
==> 10x3 = 1250m3
==> x3 = 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(250m2 + 50m2 + 125m2 )
= 2 × 425m2
= 850 m2
you could use this cuemath surface area of a cuboid calculator to verify the answer.