Page 295 - Start Up Mathematics_8 (Non CCE)

10. A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being
4.8 cm. Find its: (a) inner curved surface area (b) outer curved surface area (c) total surface area
11. A cylindrical vessel open at the top has a base diameter of 21 cm and height 14 cm. Find the cost
2
of tin plating its inner part at the rate of ` 5 per 100 cm .

MATHS LAB ACTIVITY

Objective: To find the formula for lateral surface area of a cylinder
Material required: A cylindrical object, coloured paper, pencil, a pair of scissors, scale, glue
stick/fevicol
Step 1: Take a coloured sheet of paper and cut a rectangle with
width equal to the height of the cylindrical object.
Step 2: Now paste one end of this rectangle on the cylindrical
object and wrap it along its curved surface till you
reach the starting point. h
Step 3: Cut off the extra paper. Now remove the rectangular r
strip from the cylindrical object. You will see that the
length of the rectangular strip is the circumference of
the base of the cylinder. D C
Now area of rectangle = AB × BC = (2πr) × h = 2πrh
Observation: The lateral surface area of a cylinder h
is 2πrh.
The above experiment can also be done by making a
stack of 10–15 one rupee coins.
A 2pr B
A ` 1 coin is circular in shape and its circumference is 2πr.
Measure the height of the coins in the stack (h), 2πr + 2πr
+ 2πr + ... upto the number of coins. The curved surface
area will be 2πr × h.

Volume of a Cylinder r

Let there be a cylinder with radius r unit and height h unit (Fig. 18.5).
Volume of the right circular cylinder = Area of the base × height
h
2
= (pr × h) cubic units
2
= pr h cubic units r
Fig. 18.5
Volume of a hollow cylinder r
Let there be a hollow cylinder with external and internal radii R and r
respectively and height h (Fig. 18.6).
h
Volume of the hollow cylinder = External volume – Internal volume
2
2
= (pR h – pr h) cubic units
R
2
2
= ph(R – r ) cubic units Fig. 18.6
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