Question

The perimeter of a godown is 240m. Length of the godown is twice its breadth. Find the storage capacity of the godown if the walls of the godown are 8m high.

Answer 1

Hint: Use perimeter of rectangle = 2(l+b), where l is the length and b is the breadth. Hence find the length and breadth. Use the volume of cuboid = lbh to find the volume of the cuboid.

Complete step-by-step answer:
 Let “b” be the breadth of the cuboid. So we have length = 2b as the length is twice the breadth.
Now we know that perimeter of base = 2(l+b) = 2(2b+b) = 6b.
But given that the perimeter of the base of the cuboid is 240m.
Hence we have 6b = 240.
Dividing both sides by 6, we get
b = 40m
Hence l = 2(40) = 80m.
Hence the length of the cuboid = 80m and the breadth = 40m.
Given that the height of the cuboid equals 8m.
Hence we have
The volume of cuboid = lbh $=80\times 40\times 8=25600$ cubic metres,
Hence the capacity of the godown = 256000 cubic metres.

Note: [1] The base of the cuboid is a rectangle. In a rectangle perimeter = 2(l+b). Hence we have used that the perimeter of the base = 2(l+b).
[2] A cuboid is a special case of a prism. In a prism volume = area of base$\times $ height.
Since in a cuboid, the base is rectangular, area of base = lb.
Hence the volume of cuboid = lbh.