The volumes of two similar cylinders.

Question

The two cylinders have the same heights and the radius of the cylinder B is two times the radius of cylinder A. The volume of A is $1$ and we're interested in the volume of cylinder B. Since The formula for volume is $V=\pi r^2h$, then the volume of the second cylinder should quadruple, because twice the radius will be squared. Am I correct?

Answer 1

You have correctly identified the two objects are not similar.

However, the two bases are still similar because they both are circles.

Therefore, $\dfrac {A_1}{A_2} = (\dfrac {r_1}{r_2})^2 = … = \dfrac {1}{4}$.

Then, $\dfrac {V_1}{V_2} = \dfrac {A_1 \cdot h}{A_2 \cdot h} = \dfrac {1}{4}$.

Answer 2

Yes, that is correct. When stating an example like this I avoid factors of two to avoid confusion caused by the fact that $2+2=2 \cdot 2=2^2$ If the radius triples, the volume goes up nine times.