Question

Two cuboids with equal volumes will always have equal surface areas.

Options

• True

• False

Answer 1

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.