Question

if the radii and heights of a cylinder and a cone are equal then volume of this cylinder will be how many times of the volume of the cone?​

Answer 1

Answer:

Let the radius of both the cylinder and cone be R and the height be H.

Volume of Cylinder = πr²h

Volume of Cone = 1/3 (πr²h)

Substituting the Radius R and Height H, we get:

⇒ Volume of Cylinder = πR²H

⇒ Volume of Cone = 1/3 ( πR²H)

Taking the Ratio we get:

$\implies \dfrac{ \text{ Volume of Cylinder } }{ \text{ Volume of Cone } } = \dfrac{ \pi R^2 H}{ (1/3) \pi R^2 H}\\\\\\\implies \dfrac{ \text{ Volume of Cylinder } }{ \text{ Volume of Cone } } = \dfrac{ 1 }{ 1/3 }\\\\\\\implies \dfrac{ \text{ Volume of Cylinder } }{ \text{ Volume of Cone } } = 1 \times \dfrac{3}{1}\\\\\\\implies \dfrac{ \text{ Volume of Cylinder } }{ \text{ Volume of Cone } }= \dfrac{3}{1}$

$\text{ Cross multiplying we get: }\\\\\\\implies \boxed{ \bf{ \textbf{Volume of Cylinder } \times 1 = 3 \times \textbf{Volume of the cone} } }$

Therefore the Volume of the Cylinder will be 3 times the Volume of the Cone.

Answer 2

Answer:

Required Answer :-

Let the radius of both the cylinder and cone be R and the height be H.

Let the Volume of Cylinder be V and Volume of cone be V'

V/V' = πR²H/⅓πR²h [π get cancelled]

V/V' = R²H/⅓R²H

V/V' = H/⅓H

V/V' = 1/(⅓)

V/V' = 1 × 3/1

V/V' = 3/1

$\dag {\boldsymbol { \pink{By \: Cross \: Multiplication}}}$

V × 1 = 3 × V'

Hence :-

Volume of the Cylinder should be 3 times the Volume of the Cone.