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प्रश्न
A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.
उत्तर
Given that:
Radius of the base `r=d/2=20/2=10 m`
Height of the cylinder h1 = 2.5 m
Height of the cone h2 = 7.5 m
Slant height of the cone
`l = sqrt(r^2+h^2)`
`=sqrt(10^2+7.5^2)`
= 12.5 m
The total capacity of the tent is given by
`V=pir^2h_1+1/3pir^2h_2`
`=rxx10^2xx2.5+1/3xxpixx10^2xx7.5`
= π x 250 + π x 250
= 500π m3
The total area of canvas required for the tent is
S = 2πrh + πrl
= 2 x 3.14 x 10 x 2.5 + 3.14 x 10 x 12.5
= π(2 x 10 x 2.5 + 10 x 12.5)
= π(50 + 125)
`= 22/7xx175`
= 550 m2
Therefore, the total cost of the canvas is
= 100 x 550
= Rs. 55000
Hence, the total capacity and cost is V = 500π m3, and Rs. 55000
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