Question

If the heights of two cones are in the ratio 1:4 and the radii of their bases are in the ratio 4:1,then the ratio of their volumes is

• A. 1:2
• B. 2:3
• C. 3:4
• D. 4:1

Answer 1

The correct option is D

4:1

Let height of the first cone = x

So, height of the second cone = 4x

Radius of the first cone = 4y

and radius of the second cone = y

Now, volume of first cone = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi x^2\times 4y=\frac{4}{3}\pi x^{2}y$

and volume of second cone = $\frac{1}{3}\pi (4x{)}^2\times y=\frac{1}{3}16x^{2}y=\frac{16}{3}\pi x^{2}y=16\left(\frac{1}{3}\pi x^{2}y\right)\therefore Ratiobetweentheirvolumes,\frac{16}{3}\pi x^{2}y:\frac{4}{3}\pi x^{2}y\Rightarrow \frac{16}{3}:\frac{4}{3}=4:1$