Question

Question 59

State whether the following statement is true or false:

Two cylinders with equal volume will always have equal surface area.

Answer 1

False
Consider two cylinders with the following measures.
e.g. $r_1=2cm$, h = 9 cm and r = 3 cm, h = 4 cm
For the first cylinder,
Volume $=\pi r^{2}h=\pi \times 2^2\times 9=36\pi c{m}^3$
Again, for the second cylinder,
Volume $=\pi r^{2}h=\pi \times 3^2\times 4$
$=36\pi c{m}^3$
$\therefore$ The volumes are equal.
Now, surface area of first cylinder $=2\pi rh=2\pi \times 2\times 9=36\pi c{m}^2$
and surface area of second cylinder $=2\pi rh=2\pi \times 3\times 4=24\pi c{m}^2$ which are not equal.
So, the statement is false.