Question : The ratio of the volume of two cylinders is 13 : 1 and the ratio of their heights is 13 : 9. If the area of the base of the second cylinder is 154 cm2, then what will be the radius of the first cylinder?
Option 1: 42 cm
Option 2: 21 cm
Option 3: 28 cm
Option 4: 14 cm
Correct Answer: 21 cm
Solution :
Volume of a cylinder = $\pi r^2 h$, where $r$ = radius , $h$ = height
It is given that the ratio of the volume of two cylinders is $\frac{V_1}{V_2} = \frac{13}{1}$
and ratio of heights is $\frac{h_1}{h_2} = \frac{13}{9}$
⇒ $\frac{V_1}{V_2} = \frac{πr_1^{2} h_1}{πr_2^{2} h_2}$
⇒ $\frac{13}{1} = \frac{πr_1^{2}}{πr_2^{2}}×\frac{13}{9}$
⇒ $\frac{13}{1} = \frac{πr_1^{2}}{154}×\frac{13}{9}$
⇒ $πr_1^{2} = 154 ×9$
⇒ $r_1^{2} = \frac{154 ×9 × 7}{22}$
$\therefore r_1=21$ cm
Hence, the correct answer is 21 cm.
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