Question

The total surface area of a cuboid is 46m². If its height is 1m and breadth 3m, find its length and volume.

Answer 1

Given that:
T.S.A. of a cuboid = 46m² .................................(1)
Height = 1m
Breadth = 3m
Let the length of cuboid = lm
We know that:-
T.S.A. of cuboid = 2 x {(l x b) + (b x h) + (h x l)} ......................(2)
On comparing (1) & (2) we get,
2 x {(l x b) + (b x h) + (h x l)} = 46
2 x {(l x 3) + (3 x 1) + (1 x l)} = 46
2 x {3l + 3 + l} = 46
2 x {4l + 3} = 46
8l + 6 = 46
8l = 46 - 6
8l = 40

l = `(40)/(8)`
l = 5m
∴ Length (l) = 5m
Now,
Volume of cuboid
= l x b x h
= 5 x 3 x 1
= 15m³.