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प्रश्न
Two cuboids with equal volumes will always have equal surface areas.
विकल्प
True
False
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उत्तर
This statement is False.
Explanation:
We discard the statement by a counter example.
Let the dimensions of two cuboids be 1 cm × 1 cm × 2 cm and 1 cm × `1/2` cm × 4 cm, respectively.
Then, volume of first cuboid = `l xx b xx h = 1 xx 1 xx 2` = 2 cm3
And volume of second cuboid = `l xx b xx h = 1 xx 1/2 xx 4` = 2 cm3
Now, the surface area of first cuboid = `2(lb + bh + hl)`
= 2(1 × 1 + 1 × 2 + 2 × 1)
= 2(1 + 2 + 2)
= 10 cm2
And surface area of the second cuboid = `2(lb + bh + hl)`
= `2(1 xx 1/2 + 1/2 xx 4 + 1 xx 4)`
= `2(1/2 + 4/2 + 4)`
= `2(5/2 + 4)`
= `2(13/2)`
= 13 cm2
Which are not equal.
So, the statement is false.
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