Question

2 cones have their heights in ratio 1:3 and radii 3:1 . what is the ratio of their volumes?

Answer 1

Hey mate!

________________

Let the height and radius of first cone be x and 3x respectively.

Volume of first cone = π r² h/3

=> π × (9x²) × ( x/3)

Now,

Let the height and radius of second cone be 3x and x respectively.

Volume of 2nd cone = π r² h/3

=> π × (x²) × (3x / 3)

Ratio of their volumes :-)


$\frac{ \cancel \pi \times 9 \cancel x { }^{2} \times \cancel{ x} / 3}{ \cancel \pi \times \cancel x {}^{2} \times 3 \cancel {x} /3} \\ \\ \frac{9 /3 }{3 /3 } = 3 : 1$


Hence,

Ratio of their volumes = 3 : 1.

__________________


Thanks for the question !

☺☺☺