Question

A cone of radius 5 cm is filled with water. If the water poured in a cylinder of radius 10 cm, the height of the water rises 2 cm, then the height of the cone is

Answer 1

$\bigstar \underline{\underline{\bf Given:-}}$

• Radius of cone = 5cm.
• If the water poured in a cylinder of radius 10 cm, the height of the water rises 2 cm.

$\bigstar \underline{\underline{\bf To\ find:-}}$

• Height of the cone.

$\bigstar \underline{\underline{\bf Solution:-}}$

We know :

-------------------------------------

❥Volume of cone=1/3 πr²h

❥Vol of cylinder =πr²h

--------------------------------------

Acc to question,

=> Vol of cone = 1/3 π(5)²h

                         =1/3π(25)h

Given that,If the water poured in a cylinder of radius 10 cm, the height of the water rises 2 cm.

Hence,

❥ Vol of cylinder = Vol of cone

$:\implies \sf \pi r^2 h = 25 /3 \pi h\\\\ :\implies \sf \pi (10^2) x 2 = 25 / 3\pi h\\\\:\implies 200 \pi = 25/3 \pi h\\\\:\implies h = 600 / 25\\\\\implies \boxed{\boxed{\sf h = 24 cm}}$

Therefore,the height of cone is 24cm.

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HOPE IT HELPS!

Answer 2

$\bigstar \underline{\underline{\bf Given:-}}$

Radius of cone = 5cm.

If the water poured in a cylinder of radius 10 cm, the height of the water rises 2 cm.

$\bigstar \underline{\underline{\bf To\ find:-}}$

Height of the cone.

$\bigstar \underline{\underline{\bf Solution:-}}$

We know :

-------------------------------------

❥Volume of cone=1/3 πr²h

❥Vol of cylinder =πr²h

--------------------------------------

Acc to question,

=> Vol of cone = 1/3 π(5)²h

                         =1/3π(25)h

Given that,If the water poured in a cylinder of radius 10 cm, the height of the water rises 2 cm.

Hence,

❥ Vol of cylinder = Vol of cone

$:\implies \sf \pi r^2 h = 25 /3 \pi h\\\\ :\implies \sf \pi (10^2) x 2 = 25 / 3\pi h\\\\:\implies 200 \pi = 25/3 \pi h\\\\:\implies h = 600 / 25\\\\\implies \boxed{\boxed{\sf h = 24 cm}}$

Therefore,the height of cone is 24cm.

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HOPE IT HELPS!