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Question
The surface area of the three coterminus faces of a cuboid are 6, 15 and 10 cm2 respectively. The volume of the cuboid is ______.
Options
30 cm3
40 cm3
20 cm3
35 cm3
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Solution
The surface area of the three coterminus faces of a cuboid are 6, 15 and 10 cm2 respectively. The volume of the cuboid is 30 cm3.
Explanation:
If l, b and h are the dimensions of the cuboid. Then,
Volume of the cuboid = `l xx b xx h`
Here, `6 = l xx b`
`15 = l xx h`
`10 = b xx h`
∴ `6 xx 15 xx 10 = l^2b^2h^2`
∴ Volume = `l xx b xx h`
= `sqrt(6 xx 15 xx 10`
= 30 cm3
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