If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be
(a) tripled
(b) constant
(c) one sixth
(d) one third
Solution:
The curved surface of a cylinder = 2πrh
Where
r = radius of cylinder
h = height of the cylinder
Now if the radius is tripled i.e.
r’ = 3r
New Height =h’
New Curved surface area = 2πr’h’ = 2π(3r)h’ = 6πrh’
To make the new curved surface area equal to original surface area the height will have to change:
6πrh’ = 2πrh
h’ = 2πrh/6πr
h’ = h/3
Therefore the new height will be one third of the original height and only then the curved surface area will remain the same.
Answer is choice(d)
✦ Try This: If the radius of a cylinder is doubled but its curved surface area is unchanged, then its height will be (a) half, (b) constant, (c) one sixth, (d) one third
The curved surface of a cylinder = 2πrh
Where
r = radius of cylinder
h = height of the cylinder
Now if the radius is tripled i.e.
r’ = 2r
New Height =h’
New Curved surface area = 2πr’h’ = 2π(2r)h’ =4πrh’
To make the new curved surface area equal to original surface area the height will have to change:
4πrh’ = 2πrh
h’ = 2πrh/4πr
h’ = h/2
Therefore the new height will be half of the original height and only then the curved surface area will remain the same.
Answer is choice(a)
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 12
If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be (a) tripled (b) constant(c) one sixth (d) one third
Summary:
If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be one third of the original height
☛ Related Questions:
visual curriculum