Answered

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If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height, then find the ratio of the curved surface areas of the new cylinder to that of the original cylinder.​

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SalmonWorldTopper

Given info:-If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.

Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?

Explanation:-

Let the radius of the right circular cylinder be r units

Let the radius of the right circular cylinder be h units

Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)

If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units

The height of the new right circular cylinder

= (1/4)×h units

⇛ h/4 units

Curved Surface Area of the new cylinder

= 2π(2r)(h/4) sq.units

⇛ 4πrh/4 sq.units

⇛ πrh sq.units --------(ii)

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder

⇛ πrh : 2πrh

⇛ πrh / 2πrh

⇛ 1/2

⇛ 1:2

Therefore the ratio = 1:2

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2

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