Question

If the heights of two cones are in the ratio of 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

Option : (D)

\(\frac{h_1}{h_2}=\frac{1}{4}\)

\(\frac{r_1}{r_2}=\frac{4}{1}\) 

= \(\frac{v_1}{v_2}\) = \(\frac{\frac{1}{3}\pi r^2_1 h_1}{\frac{1}{3}\pi r^2_2 h_2}\)

= \(\frac{16}{1}\times\frac{1}{4}\)

= \(\frac{4}{1}\)