Question : If the ratio of the volumes of two cylinders is 6 : 5 and the ratio of their heights is 5 : 24, then what is the ratio of their radii?
Option 1: 12 : 7
Option 2: 5 : 6
Option 3: 1 : 2
Option 4: 12 : 5
Correct Answer: 12 : 5
Solution :
Given: the ratio of the volumes of two cylinders is 6 : 5 and the ratio of their heights is 5 : 24.
Let their radii be $r_1$ and $r_2$, also let their heights be $5h$ and $24h$.
According to the question,
$\frac{\pi×r_1^2×5h}{\pi×r_2^2×24h}=\frac{6}{5}$
⇒ $\frac{r_1^2}{r_2^2}=\frac{144}{25}$
⇒ $\frac{r_1}{r_2}=\frac{12}{5}$
$\therefore r_1:r_2=12:5$
Hence, the correct answer is 12 : 5.
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