Question

- A cylinder and cone have bases of equal radii and are of equal heights. Show that their
manufactured from that pap
volumes are in the ratio of 3:1.​

Answer 1

GIVEN:

• A cylinder and cone have bases of equal radii and are of equal heights.

TO FIND:

• Show that their volumes are in the ratio 3:1 ?

SOLUTION:

✒ We have given that, the radius of cone and cylinder is equal and height of cone and cylinder is same.

Let the radius of cylinder and cone be 'r' cm and height of cylinder and cone be 'h' cm

To find the volume of cylinder and cone, we use the formula:-

❰ Vol. of Cylinder = πr²h ❱

❰ Vol. of Cone = $\bf{\dfrac{1}{3}}$ πr²h❱

✍ We need to show the volume of cylinder and cone are in the ratio 3:1

According to question:-

➝ $\sf{\dfrac{Vol. \: of \: Cylinder}{Volume \: of \: cone}}$

➝ $\sf{\dfrac{ \cancel{\pi r^2 h}}{ \frac{1}{3} \cancel{\pi r^2 h}}}$

➝ $\sf{\dfrac{1 \times 3 }{1}}$

➝ $\sf{\dfrac{3}{1}}$

❝ Hence, the volume of cylinder and cone are in the ratio 3:1 ❞

______________________

Answer 2

Qᴜᴇsᴛɪᴏɴ :

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

Pʀᴏᴠᴇᴅ :

➥ The volume of the cylinder and cone are in the ratio is 3:1.

Gɪᴠᴇɴ :

➤ A cylinder and cone have bases of equal radii and are of equal heights.

Tᴏ Sʜᴏᴡ :

➤ The volume of the cylinder and cone are in the ratio of 3:1 ?

Sᴏʟᴜᴛɪᴏɴ :

Here radius is r and height is h for both of the cases.

Volume of cylinder = πr²h

Volume of cone = $\sf{\dfrac{1}{3}}$πr²h

Now, Ratio of their volumes

Volume of cylinder : Volume of cone

☛ On putting formula

$:\implies$ πr²h : $\sf{\dfrac{1}{3}}$πr²h

$:\implies$ 1 : $\sf{\dfrac{1}{3}}$

$:\implies$ $\underline{\overline{\boxed{\purple{\bf{\:\:3 : 1\:\:}}}}}$ 【 PROVED 】