10. In fig. 13.12, you see the frame of a lampshade. It is to be covered with a decorative cloth.
The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. (Assume π = 22/7)
Solution:
Say h = height of the frame of lampshade, looks like cylindrical shape
r = radius
Total height is h = (2.5+30+2.5) cm = 35cm and
r = (20/2) cm = 10cm
Use curved surface area formula to find the cloth required for covering the lampshade which is 2πrh
= (2×(22/7)×10×35) cm2
= 2200 cm2
Hence, 2200 cm2 cloth is required for covering the lampshade.
11. The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? (Assume π =22/7)
Solution:
Radius of the circular end of cylindrical penholder, r = 3cm
Height of penholder, h = 10.5cm
Surface area of a penholder = CSA of pen holder + Area of base of penholder
= 2πrh+πr2
= 2×(22/7)×3×10.5+(22/7)×32= 1584/7
Therefore, Area of cardboard sheet used by one competitor is 1584/7 cm2
So, Area of cardboard sheet used by 35 competitors = 35×1584/7 = 7920 cm2
Therefore, 7920 cm2 cardboard sheet will be needed for the competition.
Gaurav Seth 3 years, 11 months ago
10. In fig. 13.12, you see the frame of a lampshade. It is to be covered with a decorative cloth.
The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. (Assume π = 22/7)
Solution:
Say h = height of the frame of lampshade, looks like cylindrical shape
r = radius
Total height is h = (2.5+30+2.5) cm = 35cm and
r = (20/2) cm = 10cm
Use curved surface area formula to find the cloth required for covering the lampshade which is 2πrh
= (2×(22/7)×10×35) cm2
= 2200 cm2
Hence, 2200 cm2 cloth is required for covering the lampshade.
11. The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? (Assume π =22/7)
Solution:
Radius of the circular end of cylindrical penholder, r = 3cm
Height of penholder, h = 10.5cm
Surface area of a penholder = CSA of pen holder + Area of base of penholder
= 2πrh+πr2
= 2×(22/7)×3×10.5+(22/7)×32= 1584/7
Therefore, Area of cardboard sheet used by one competitor is 1584/7 cm2
So, Area of cardboard sheet used by 35 competitors = 35×1584/7 = 7920 cm2
Therefore, 7920 cm2 cardboard sheet will be needed for the competition.
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