Curved surface area of a cylinder of radius h and height r is _______.
Solution:
The figure below shows a cylinder with radius r and height h.
The surface area of the cylinder is = 2πrh
The cross section of a cylinder is a circle the circumference of which is 2πh
Cylinder can be thought of as made of many circles on top of each other.
The height of the cylinder = r
Therefore the surface area of cylinder = Circumference of the circle × height
= 2πh × r
= 2πhr
= 2πrh
✦ Try This: If a cuboid is fitted along the length of the cylinder of radius r then one edge of the cuboid will be h and the other two will be of the length ____________.
The diagram below shows a cuboid inside the cylinder of radius r and height h
The top and bottom faces of the cuboid are squares with sides which can be calculated as below:
(2r)² = a² + a²
4r² = 2a²
a = r√2
The four sides of the top and bottom face of the inserted cuboid in the cylinder will be of the length r√2.
So the edges of the cuboid are r√2, r√2 and h.
If a cuboid is fitted along the length of the cylinder of radius r then one edge of the cuboid will be h and the other two will be of the length r√2.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 43
Curved surface area of a cylinder of radius h and height r is _______.
Summary:
Curved surface area of a cylinder of radius h and height r is 2πrh
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