Question

The surface area of cuboids is 3328 m2; its dimensions are in the ratio 4:3:2. Find the volume of the cuboids.

Answer 1

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Answer 2

Given - Surface area and the ratio of dimensions

Find - Volume of cuboids

Solution - The volume of cuboids is 12,288 metre³.

The surface area of cuboids is given by the formula = 2(length*breadth + breadth*height + height*length).

Let the length, breadth and height of cuboids be 4x, 3x and 2x.

Keeping the values in the formula-

3328 = 2(4x*3x + 3x*2x + 2x*4x)

3328 = 2(12x² + 6x² + 8x²)

3328 = 2(26x²)

3328 = 52x²

x² = 3328/52

x² = 64

x = 8.

Length = 4x

Length = 4*8

Length = 32 metres

Breadth = 3x

Breadth = 3*8

Breadth = 24 metres

Height = 2x

Height = 2*8

Height = 16 metres

The volume of cuboid = length*breadth*height.

The volume of cuboid = 32*24*16

The volume of the cuboid = 12,288 metre³.

So, the volume of cuboids is 12,288 metre³.