Question

If the radius of a cylinder is doubled and height is halved, how many times will be its new volume?​

Answer 1

GIVEN :-

• Radius of the cylinder is doubled and height is halved.

TO FIND :-

• By how many tims , Volume of the cylinder is increased.

TO KNOW :-

★ Volume of Cylinder = πr²h

Here ,

• r is Radius of Cylinder.
• h is Height of Cylinder.

SOLUTION :-

Let Radius of Cylinder be 'r' and height be 'h'.

So, volume of cylinder will be

→ V = πr²h -------(1)

Now , Radius is doubled and height is halved.

• New radius = 2r
• New height = h/2

→ Volume (V') = π(2r)²(h/2)

→ V' = π(4r²)(h/2)

→ V' = π(2r²h)

→ V' = 2(πr²h) -------(2)

By equation (1) , πr²h = V

Putting in equation (2),

→ V' = 2V

Therefore , Volume is doubled when radius is doubled and height is halved.

MORE TO KNOW :-

★ Volume of Cube = edge³

★ Volume of Cuboid = l × b × h

★ Volume of Cone = (1/3)πr²h

★ Volume of Sphere = (4/3)πr³

★ Volume of Hemisphere = (2/3)πr³