Page 184 - Maths Skills - 8

182 Maths

If the axis of a cylinder is perpendicular to the bases, then the cylinder is called a right circular cylinder.
Or

A solid generated by the rotation of a rectangle about one of its sides is called a right circular cylinder.
Fig. (ii) is a right circular cylinder.

SURFACE AREA AND VOLUME OF A CYLINDER

Surface Area of a Cylinder
Take a cylinder of height h and radius r as shown in Fig. Cut it along a line on the surface parallel to axis of the
cylinder and unfold it. What do you obtain? A rectangle of length 2πr and breadth h.

\ Area of the curved surface of a cylinder = Area of the rectangle 2πr
= 2πr × h sq. units
h
= 2πrh sq. units
\ Total surface area of a cylinder

= Area of the curved surface + 2 × base area
= 2πrh + 2πr = 2πr(h + r) sq. units.
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Volume of a Cylinder
We know that the volume of a cuboid = length × breadth × height
= (length × breadth) × height

= Area of the base × height
The same formula applies to the volume of a cylinder
\ Volume of a cylinder = Area of the base × height
= πr × h cubic units
2
= πr h cubic units.
2

Let’s Attempt

Example 1: A rectangular piece of paper of dimensions 44 cm by 10 cm is rolled along its length to form a
cylinder. Find the volume of the cylinder so formed.
Solution: Here, height of the cylinder = 10 cm and total length, i.e., circumference of its base = 44 cm.
Let r be the radius of the base.
\ 2πr = 44 cm ⇒ r = 44
2π
44 × 7 22
⇒ r = 2 × 22 = 7 cm [ π = 7 ]
\ Volume of the cylinder formed = πr h cubic units
2
22
= × 7 × 7 × 10 cm = 1540 cm .
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Example 2: Find the volume and the total surface area of a cylinder of height 21 cm and radius 14 cm.
Solution: Here, r = 14 cm and h = 21 cm.
22
Volume of the cylinder = πr h cubic units = 14 14 21 cm = 12936 cm .
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