If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true?
(a) Curved surface area of the cylinder will be doubled.
(b) Curved surface area of the cylinder will remain unchanged.
(c) Curved surface area of the cylinder will be halved.
(d) Curved surface area will be 1/4 of the original curved surface

Solution:

The curved surface area of a cylinder(S) = 2πrl

r = radius of the cylinder

l = length or height of the cylinder

If the height of the cylinder is reduced to 1/4th of the original height and radius is doubled then,

h’ = h/4 and r’ = 2r

Curved surface area (S’) = 2π(2r)(l/4)

S’ = πrl

The new curved surface area is half of the original curved surface area.

The correct answer is (c ).

✦ Try This: If the height of a cylinder becomes 1/2 of the original height and the radius remains same, then which of the following will be true?

(a) Curved surface area of the cylinder will be doubled.

(b) Curved surface area of the cylinder will remain unchanged.

(c) Curved surface area of the cylinder will be halved.

(d) Curved surface area will be 1/4 of the original curved surface.

The curved surface area of a cylinder(S) = 2πrl

r = radius of the cylinder

l = length or height of the cylinder

If the height of the cylinder is reduced to 1/2 of the original height and radius is kept same then,

h’ = h/2 and r’ = r

Curved surface area (S’)= 2π(r)(l/2)

S’ = πrl

The new curved surface area is half of the original curved surface area.

The correct answer is (c).

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

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NCERT Exemplar Class 8 Maths Chapter 11 Problem 6

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true? (a) Curved surface area of the cylinder will be doubled.(b)Curved surface area of the cylinder will remain unchanged.(c) Curved surface area of the cylinder will be halved.(d) Curved surface area will be 1/4 of the original curved surface

Summary:

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then the curved surface area of the cylinder will be halved

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