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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Assume that a cylinder is cut along its height. Also, the top and the bottom circular faces are cut
separately. Thus, a cylinder consists of two identical circles with radius r and a rectangular strip
of width h and length 2pr (length of the circle).

r r area = pr 2
r r 2pr
+
h h area = 2prh

+
r r area = pr 2
Therefore, the curved (lateral) surface area of a cylinder will be the area of the rectangular strip.

So, curved (lateral) surface area of a cylinder = Area of rectangular strip = Length of the strip × width
= 2pr × h [Length of the strip = Circumference of the circular face]
= 2prh

Thus, the curved (lateral) surface area of a cylinder = 2prh sq. units.
Now, the total surface area of a cylinder = Area of flat face (top) + area of flat face(bottom)
+ area of curved face
2
2
= pr + pr + 2prh = 2pr(r + h)
Thus, the total surface area of a cylinder = 2pr(r + h) sq. units.
Here, the value of p is taken as 22 unless otherwise stated.
7
Example 21: Find the curved surface area and the total surface area of a cylinder having 8 cm
a radius of 8 cm and height 28 cm.
Solution: Here, radius (r) of the cylinder = 8 cm, and height (h) = 28 cm. 28 cm

We have, the curved surface area of a cylinder = 2prh
22
= 2 × × 8 cm × 28 cm = 1408 cm 2
7
Now, the total surface area of a cylinder = 2pr(r + h)
22
+
= 2 × × 8 cm ×( 8 28) cm
7 Quick Check
22 2
= 2 × × 8 cm × 36 cm = 1810 cm 2 Find curved and total
7 7 surface area of the following
Thus, the curved surface area of the given cylinder is 1408 cylinders.
2
2
2
cm and the total surface area of the cylinder is 1810 cm . 14 cm
7 1.
Example 22: Find the height of a cylinder whose radius is 8 cm
2
7 cm and lateral surface area is 1056 cm .
Solution: We have, radius of the cylinder, r = 7 cm, and curved 2. 2 m
surface area of cylinder = 1056 cm 2
\ 2prh = 1056 cm 2 2 m
1056 1056 528
2
⇒ h = cm = cm = cm = 24 cm.
2πr 2 × 22 × 7 22
7

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