Question : The radii of two cylinders are in the ratio 1 : 4 and their heights are in the ratio 4 : 3. Their volumes will be in the ratio ______.
Option 1: 1 : 12
Option 2: 2 : 9
Option 3: 3 : 10
Option 4: 1 : 9
Correct Answer: 1 : 12
Solution :
Let the radii of the 1st and 2nd cylinders be $x$ and $4x$ and their heights be $4y$ and $3y$, respectively.
Volume of 1st cylinder : volume of 2nd cylinder
$\pi r_1^2 h_1:\pi r_2^2 h_2$
$=\pi x^2\times 4y:\pi (4x)^2\times 3y$
$=x^2\times 4y:(4x)^2\times 3y$
$=1:12$
Hence, the correct answer is 1 : 12.
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