Question

the base radius of two right circular cones of the same height are in the ratio of 3:5.Find the ratio of their volumes ​

Answer 1

SOLUTION :-

Let,

Radius of the first cone ( $\sf r_1$ ) = 3x

Radius of the second cone ( $\sf r_2$ ) = 5x

Height of the two cones = h

$\bullet$ Volume of the first cone = $\sf\dfrac{1}{3}\pi (r_{2})^2h$

$\bullet$ Volume of the second cone = $\sf \dfrac{1}{3}\pi( r_{2})^2h$

$\longrightarrow\sf\dfrac{Volume \ of \ the \ first \ cone}{Volume \ of \ the \ second \ cone } \\\\\longrightarrow\dfrac{\dfrac{1}{3}\times \pi \times (r_1)^2\times h}{\dfrac{1}{3} \times \pi \times (r_2)^2\times h} \\\\\longrightarrow \dfrac{\dfrac{1}{3}\times \pi \times 3x \times 3x \times h}{\dfrac{1}{3} \times \pi \times 5x \times 5x \times h}\\\\\longrightarrow \dfrac{3x\times 3x}{5x\times 5x} \\\\\longrightarrow \dfrac{9x^2}{25x^2} \\\\\longrightarrow\bf \dfrac{9}{25}$

Ratio of the volumes of two cones = 9 : 25