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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