Question

The base radius of a cone and a cylinder are equal if their volumes are also equal then the ratio of height of cone to the height of cylinder is

Answer 1

Given :

• Base radius of cone and cylinder are equal = x (let)
• Volume of cone and cylinder are equal= V (let)

To find :

• Height of cone : Height of cylinder

Let :

• Height of cone = h
• Height of cylinder = H

Formula used :

• Volume of cylinder = π (r²) H
• Volume of cone = (1/3) π (r²) h

Solution :

Given that volume of cone = volume of cylinder

$\sf \implies \: \dfrac{1}{3} \pi( {r}^{2} )h \: = \: \pi ({r}^{2} )H \\ \\ \sf \implies \: \dfrac{h}{H} \: = 3 \times \dfrac{\pi}{\pi} \times \dfrac{ {r}^{2} }{ {r}^{2} } \\ \\ \sf \implies \dfrac{h}{H} \: = \: \dfrac{3}{1} \\ \\ \sf \implies \bold{h \: : H \: = \: 3 : \: 1 }$

ANSWER : Height of cone : Height of cylinder = 3 : 1

ANSWER