Question

in a cylinder radious is double and height is half the curved surface area will be​

Answer 1

Given :

• The radius is doubled
• The height is halved

To find :

• The new Curved Surface Area (CSA) of the cylinder.

Solution :

Let the original Radius of the base of cylinder be r , original height be h and original CSA be A unit² .

The CSA of cylinder is given by the formula :

$\large{\boxed{ \sf{\red{ csa }\: \blue{of}\: \green{cylinder} = \orange{2 \pi \: rh}}}}$

• A = 2πrh _______(1)

A/Q ,

Let new radius and height be r' and h' respectively.

• When the radius is doubled and height is halved , the new radius becomes 2r and new height becomes h/2 .

Let the new CSA be A' unit² .

A' = 2 π r' h'

A' = 2 π 2r × h/2

• A' = 2πrh _______(2)

Comparing equation 1 and 2

A'/A= 2πrh/2πrh

A' / A= 1

A' = A

Therefore , there will be no change in the Curved Surface Area of cylinder when the radius is doubled and height is halved simultaneously.

Answer 2

Answer:

Given :

• The radius is doubled

• The height is halved

To find :

• The new Curved Surface Area (CSA) of the cylinder.

Solution :

• Let the original Radius of the base of cylinder be (r).

• original height be (h)

• original CSA be (a unit square)

.

The CSA of cylinder is given by the formula :

$\sf\boxed{ \boxed{{A \: = \: 2\pi rh}}}$

• Let new radius and height be r' and h' respectively.

When the radius is doubled and height is halved , the new radius becomes 2r and new height becomes h/2 .

Let the new CSA be A' unit² :

A' = 2 π r' h'

A' = 2 π 2r × h/2

A' = 2πrh _______(2)

Comparing equation 1 and

A'/A= 2πrh/2πrh

A' / A= 1

A' = A

Therefore , there will be no change in the Curved Surface Area of cylinder when the radius is doubled and height is halved simultaneously.