The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the ratio between the height and radius of the cylinder.
Solution:
Curved surface area of a cylinder = 2πrh
Total Surface area of right circular cylinder = 2πr² + 2πrh
2πrh/(2πr² + 2πrh) = 1/2
h/r + h = 1/2
2h = r + h
2h - h = r
h = r
h/r = 1:1
The ratio between height and radius is 1:1.
✦ Try This: The ratio between the curved surface area and the total surface area of a right circular cylinder is 2:3. Find the ratio between the height and radius of the cylinder.
Curved surface area of a cylinder = 2πrh
Total Surface area of right circular cylinder = 2πr² + 2πrh
2πrh/(2πr² + 2πrh) = 2/3
h/r + h = 2/3
3h = 2r + 2h
3h - 2h = 2r
h = 2r
h/r = 2:1
The ratio between height and radius is 2:1.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 119
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the ratio between the height and radius of the cylinder.
Summary:
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. The ratio between the height and radius of the cylinder is 1:1
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