Question

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

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Consider two cylinders with the following measures

E.g. r₁ = 2 cm, h = 9 cm and r = 3 cm, h = 4 cm

For the first cylinder,

Volume = πr²h = π × 2² × 9 = 36 π cm³

Again, for the second cylinder,

Volume = πr²h = π × 3² × 4 = 36 π cm³

∴ The volumes are equal.

Now, surfaces area of first cylinder = 2πh = 2π × 2 × 9 = 36 π cm²

And surface area of second cylinder = 2πrh = 2π × 3 × 4 = 24 π cm²

Which are not equal.

So, the statement is false.