Question : If the heights of two cylinders are in the ratio of 7 : 9 and their diameters are in the ratio of 6 : 7, then what is the ratio of the volumes of the cylinders?
Option 1: 6 : 7
Option 2: 7 : 9
Option 3: 5 : 9
Option 4: 4 : 7
Correct Answer: 4 : 7
Solution :
The ratio of heights of two cylinders = 7 : 9
Ratio of diameters = ratio of radii = 6 : 7
Ratio of volumes of two cylinders
= $\frac{\frac{4}{3}\pi r_1^2h_1}{\frac{4}{3}\pi r_2^2h_2}$
= $\frac{r_1^2h_1}{r_2^2h_2}$
= $\frac{6^2×7}{7^2×9}$
= $\frac{4}{7}$
= 4 : 7
Hence, the correct answer is 4 : 7.
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