Question : The radii of two cylinders are in the ratio of 4 : 5 and their heights are in the ratio of 5 : 2. The ratio of their volume is:
Option 1: 9 : 4
Option 2: 2 : 1
Option 3: 9 : 7
Option 4: 8 : 5
Correct Answer: 8 : 5
Solution :
Given,
The radii of two cylinders are in the ratio of 4 : 5 and their heights are in the ratio of 5 : 2.
We know,
The volume of cylinder = $\pi r^2h$, where $r$ is the radius and $h$ is the height.
⇒ $\frac{V_1}{V_2}=\frac{r_1^2h_1}{r_2^2h_2}$, where $V_1$ and $V_2$ are the volume of two cylinders
⇒ $\frac{V_1}{V_2}=(\frac{4}{5})^2(\frac{5}{2})$
⇒ $\frac{V_1}{V_2}=\frac{4\times4\times5}{5\times5\times2}$
⇒ $\frac{V_1}{V_2}=\frac{2\times4}{5}$
⇒ $\frac{V_1}{V_2}=\frac85$
Hence, the correct answer is 8 : 5.
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