NCERT Class 9 Mathematics

SURFACE AREAS AND VOLUMES 215

Fig. 13.8
The area of the sheet gives us the curved surface area of the cylinder. Note that
the length of the sheet is equal to the circumference of the circular base which is equal
to 2✁r.

So, curved surface area of the cylinder

= area of the rectangular sheet = length × breadth

= perimeter of the base of the cylinder × h

=2✁r × h

Therefore, Curved Surface Area of a Cylinder = 2✁✁rh

where r is the radius of the base of the cylinder and h is the height of the cylinder.

Remark : In the case of a cylinder, unless stated
otherwise, ‘radius of a cylinder’ shall mean’ base radius
of the cylinder’.

If the top and the bottom of the cylinder are also to
be covered, then we need two circles (infact, circular
regions) to do that, each of radius r, and thus having an
area of ✁r^2 each (see Fig. 13.9), giving us the total
surface area as 2✁rh + 2✁r^2 = 2✁r(r + h).

So, Total Surface Area of a Cylinder = 2✁✁✁✁r(r + h)

where h is the height of the cylinder and r its radius.

Remark : You may recall from Chapter 1 that ✁ is an irrational number. So, the value

Fig. 13.9