Question

Question 56

State whether the following statement is true or false:

​​​​​​​Two cuboids with equal volume will always have equal surface area.

Answer 1

False
We discard the statement by a counter example.
Let the dimensions of two cuboids be $1cm\times 1cm\times 2cm$ and $1cm\times \frac{1}{2}cm\times 4cm$ respectively.
Then, volume of first cuboid $=l\times b\times h=1\times 1\times 2=2c{m}^3$
and volume of second cuboid $=l\times b\times h=1\times \frac{1}{2}\times 4=2c{m}^3$
Now, the surface area of first cuboid $=2(lb+bh+hl)$
$=2(1\times 1+1\times 2+2\times 1)$
$=2(1+2+2)=10c{m}^2$
and surface area of the second cuboid $=2(lb+bh+hl)$
$=2(1\times \frac{1}{2}+\frac{1}{2}\times 4+1\times 4)=2(\frac{1}{2}+\frac{4}{2}+4)$
$=2(\frac{5}{2}+4)=2\left(\frac{13}{2}\right)=13c{m}^2$
which are not equal.
So, the statement is false.