Question : If the ratio of the volumes of two cylinders is 7 : 5 and the ratio of their heights is 5 : 7, then what is the ratio of their radii?
Option 1: 5 : 7
Option 2: 3 : 4
Option 3: 5 : 9
Option 4: 4 : 5
Correct Answer: 5 : 7
Solution :
According to the question,
$\frac{V_1}{V_2}$ = $\frac{7}{5}$
and, $\frac{h1}{h2}$ = $\frac{5}{7}$
Now, $\frac{V_1}{V_2}$ = $\frac{πr_1^{2}h_1}{πr_2^{2}h_2}$
⇒ $\frac{7}{5}$ = $\frac{5×r_1^{2}}{7×r_2^{2}}$
⇒ 49 × $r_1^{2}$ = 25 × $r_2^{2}$
⇒ $\frac{r_1}{r_2}$ = $\frac{\sqrt{25}}{\sqrt{49}}$ = $\frac{5}{7}$
Hence, the correct answer is 5 : 7.
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