The edge of the cuboid are in the ratio of 1 : 2 : 3 and its surface area is 88 cm². What will be the volume of the cuboid?

Correct Answer is : 48 cm3cm³cm3

Correct Answer is : 48 cm3cm³cm3

Test Index

Volumes Practice Test 1

Question : 6 of 40

Marks: +1, -0

cm^2

Solution: 👈: Video Solution

Concept:

Use the surface area to find the cuboid's edge lengths from the given ratio, then calculate volume.

Explanation:

Let the edges be

x

2x

, and

3x

Surface area of a cuboid is

2(lb+bh+hl)=88

Substitute the edges:

2(x\cdot2x+2x\cdot3x+3x\cdot x)=88

Simplify:

2(2x^2+6x^2+3x^2)=88

2(11x^2)=88

22x^2=88

x^2=4

x=2

So the edges are

2\ \mathrm{cm}

4\ \mathrm{cm}

, and

6\ \mathrm{cm}

Volume is

V=2\times4\times6=48\ \mathrm{cm}^3

Answer:

The volume of the cuboid is

48\ \mathrm{cm}^3

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