Page 294 - Start Up Mathematics_8 (Non CCE)

\ Length of sheet = Circumference of base = 2pr cm

Also, lateral surface area = 2prh
fi 4,224 = 2pr × 33 33 cm
4 224,
fi 2pr = = 128
33
\ Length of sheet (l) = 128 cm
Perimeter of sheet = 2(l + b) = 2(128 + 33) cm 33 cm

= 2 × 161 cm = 322 cm
\ Perimeter of rectangular sheet = 322 cm 2pr cm
Example 31: An 18 cm long iron pipe has an external diameter of 24 cm. If the thickness of the pipe is
1 cm, find the total surface area of the pipe.
Solution: External diameter of pipe = 24 cm

24
\ External radius (R) = 2 cm = 12 cm
Thickness of pipe = 1 cm
Hence, Internal radius (r) = External radius – Thickness of pipe = (12 – 1) cm = 11 cm
Length of pipe (h) = 18 cm

22
\ Total surface area of the pipe = 2 × × (12 + 11)(18 + 12 – 11)
7
22
= 2 × × 23 × 19 = 2,746.86 cm 2
7
EXERCISE 18.3

1. The radius of a right circular cylinder is 7 cm and its height is 14 cm. Find its curved surface area
and total surface area.
2
2. The curved surface area of a cylinder is 1,000 cm and the radius of its base is 21 cm. Find the total
surface area of the cylinder.
3. An open cylindrical oil tank has diameter 14 m and height 9 m. If the inner side of the tank has to
be painted all over, what will it cost at ` 40 per square metre?
4. The inner diameter of a circular well is 3.5 m and it is 12 m deep. Find the cost of plastering the
inner surface at the rate of ` 4 per square metre.
5. It costs ` 2,200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If it is painted at
the rate of ` 20 per square metre, find:
(a) the inner curved surface area of the vessel (b) the radius of the base
6. A cylindrical road roller is of length 2 m and diameter 84 cm. Find the number of revolutions it has
2
to make to cover an area of 7,920 m .
7. The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 5 : 3. Find the ratio
of their curved surface areas.
8. Some fruits are sliced and packed into cylindrical cans of height 32 cm and diameter of base 20 cm.
A label is placed around the curved surface of the can by leaving a margin of 2 cm from the top and
bottom of the can. Find the surface area of the label.
9. A school organized a competition of making and decorating pen holders in the shape of a cylinder
by making its base and its curved surface area with cardboard. Each pen holder is supposed to have
a radius of 3.5 cm and height 10 cm. How much cardboard does the school need if 30 students are
participating in the competition?

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