# If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved. Is the given statement true or false and justify your answer.

**Solution:**

Given, if the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

We have to determine if the given statement is true or false.

Curved surface area of the cylinder = 2πrh

Where, r is the radius of the cylinder

h is the height of the cylinder

Given, r = 2r

h = h/2

Now, curved surface area = 2π(2r)(h/2)

= 2πrh

Therefore, the given statement is true.

**✦ Try This: **If the radius of a cylinder is doubled, the height remains unchanged. Find the curved surface area of the cylinder.

Given, the radius of the cylinder is doubled

We have to find the curved surface area of the cylinder

Curved surface area of the cylinder = 2πrh

Where, r is the radius of the cylinder

h is the height of the cylinder

Given, r = 2r

Now, curved surface area = 2π(2r)(h)

= 4πrh

Therefore, the curved surface area = 4πrh square units.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 13

**NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 4**

## If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved. Is the given statement true or false and justify your answer.

**Summary:**

The given statement “If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved” is true

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