# If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged. Is the given statement true or false and justify your answer.

**Solution:**

Given, the radius of a right circular cone is halved and height is doubled

The volume will remain unchanged

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

Volume of the cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Given, r = r/2

h = 2h

So, volume = 1/3 π(r/2)²(2h)

= 1/3 π(r²/4)(2h)

= 1/3 π(r²/2)h

= 1/6 πr²h

There is a change in volume.

Therefore, the given statement is false.

**✦ Try This: **If the radius of a right circular cone is doubled and height is tripled, the volume is

Given, the radius of a right circular cone is doubled and height is tripled

We have to determine the volume of the cone

Volume of the cone = 1/3 πr²h

Where, r is the radius of the cone

h is the height of the cone

Given, r = 2r

h = 3h

So, volume = 1/3 π(2r)²(3h)

= π(4r²)(h)

= 4πr²h

Therefore, the volume is 4πr²h cubic units.

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

**NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 2**

## If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged. Is the given statement true or false and justify your answer.

**Summary:**

The given statement “If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged” is false

**☛ Related Questions:**

- In a right circular cone, height, radius and slant height do not always be sides of a right triangle . . . .
- If the radius of a cylinder is doubled and its curved surface area is not changed, the height must b . . . .
- The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals t . . . .

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