EXAMPLE 4
Due to some floods, some welfare associations jointly requested the
government to get 100 tents fixed immediately and offered to
contribute 50% of the cost. If the lower part of each tent is of the form
of a cylinder of diameter 4.2 m and height 4 m with the conical upper
part of same diameter but of height 2.8 m, and the canvas to be used
costs 100 per square metre, find the amount the associations will
have to pay. What values are shown by these associations?
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9th
Maths
Surface Areas and Volumes
Volume of Cone
Due to sudden floods, some ...
MATHS
Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of the same diameter but height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations [Useπ=
7
22
]
October 15, 2019
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Sukhpreet Sameria
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ANSWER
Given height of cylindrical part =4 m
And height of conical pert =2.8 m
Diameter of cylindrical part = Diameter of conical part =4.2 m
Radius of cylindrical part = Radius of conical part =2.1 m
The surface area of cylindrical part =2πrh
=2×
7
22
×2.1×4=2×22×0.3×4=52.80 m
2
Surface area of conical part =π×r×
r
2
+h
2
=
7
22
×2.1×
(2.8)
2
+(2.1)
2
=22×0.3×
7.84+4.41
=6.6×
12.25
=6.6×3.5=23.10 m
2
The surface area of tent = Surface area of cylindrical part + Surface area of conical part =52.80+23.10=75.90 m
2
Surface area of 100 tent =75.90×100=7590 m
2
Cost of 100 tent =100×7590=Rs 759000
But 50% cost have to paid by association.
Association have to pay :
100
759000
×50=Rs 379500
Radius of the cylinder, r = 2.1 m
Height of the cylinder, h = 4 m
Radius of the cone = radius of the cylinder = 2.1 m
Height of the cone, H = 2.8 m
Slant height of the cone, I = VP+H?
(21)' +(28) m
4.41 +784 m
- 12.25 m 35 m.
Area of the canvas required for each tent
= curved surface area of the cylinder
+ curved surface area of the cone
22
= 27th + ferl 2x x 2.1 x 4 + x 21 x 35
2 1 m
1 m
m
(52.8 + 23.1) m = 75.9 m
Total area of the canvas required for 100 tents
(759 x 100) m =7590 m
Total cost of 100 tents (7590 x 100) 759000.
Amount to be paid by the associations
50
50% of 759000 = x 759000379500.
100
Hence, the associations will have to pay 379500.