Question

If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ration of their heights is

• A. 25 : 64
• B. 5 : 4
• C. 64 : 25
• D. 5 : 16

Answer 1

The correct option is A 25 : 64

$=\frac{\frac{1}{3}\pi (2{)}^2{h}_1}{\frac{1}{3}\pi {\left(\frac{5}{2}\right)}^2{h}_2}=\frac{1}{4}$
$=\frac{4h_1}{\frac{4h_1}{\frac{25}{4}{h}_2}}=\frac{1}{4}\Rightarrow \frac{16h_1}{25h_2}=\frac{1}{4}$
$\Rightarrow \frac{h_1}{h_2}=\frac{1}{4}\times \frac{25}{16}=\frac{25}{64}$