Question

A cylinder and a cone have the same height and same radius of the base. Find the ratio between the volumes of the cylinder and the cone. ​

Answer 1

SOLUTION:

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ANSWER:

• The ratio between the volumes of the cylinder and the cone is 3:1.

GIVEN:

• A cylinder and a cone have the same height and same radius of the base.

TO FIND:

• Find the ratio between the volumes of the cylinder and the cone.

SOLUTION:

Let the ratio be x

FORMULA TO FIND:

Volume of the cone = 1/3 × πr² h

Volume of a cylinder = πr²h

SOLVING BY APPLYING THE FORMULA:

= πr²h ÷ 1/3 πr²h

= πr²h × 3/πr²h

= 3πr²h/πr²h

• Cancel πr²h from both the sides.

= 3

• There is nothing on the other side. So , it will be one.

Ratio = 3:1

Hence , The ratio between the volumes of the cylinder and the cone is 3:1.

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Answer 2

Correct question:-

1. A cylinder and a cone have bases of equal radii and are equal height. Show that their volumes are in ratio 3:1.

Required answer:-

• 3:1 is the required answer

Given that,

• Volume = 3:1

To find:-

• Verification of the ratio

Answer:-

Volume of cylinder                                                    Volume of cone

  $\rm\pi r^{2} h$                                                                                  $\rm\dfrac{1}{3}\pi r^{2}h$

  $\rm\dfrac{Volume \: of \: cylinder}{ Volume \: of \: cone}=\dfrac{\pi r^{2} h}{\dfrac{1}{3} \pi r^{2} h}$

     $\rm \dfrac{1}{\dfrac{1}{3}}=1 \times \dfrac{1}{3}$

$\rm\dfrac{Volume \: of \: cylinder}{Volume \: of \:cone}$ ⇰ 3:1

         Hence verified!