This is the important question for cbse/ncert board exam in this question position of the cylinder and cone in the tent with that they give height by using surface area formulas we will get answer of this question. This question from RS Aggarwal book, exercise 17A chapter volume and surface area of solid, page number 787.
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A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs. 80 per square meter.
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The tent is made as a combination of right circular cylinder and right circular cone on top.
Height of cylindrical part of the tent = h = 3 m
Radius of its base = r = 14 m
Total height of the tent = 13.5 m
Curved surface area of cylindrical part of tent = 2πrh
= 2 × 22/7 × 14 × 3
= 264 m2
Height of conical part of the tent = total height of tent – height of cylindrical part
Height of conical part of the tent = 13.5 – 3 m =10.5 m
Let the slant height of the conical part be l.
l2 = h2 + r2 (used cone height)
= 110.25 + 196
= 306.25
or l = 17.5 m
Curved surface area of conical part of tent = πrl
= 22/7 × 14 × 17.5
= 770
Total surface area of tent = Curved surface area of cylindrical part of tent + Curved surface area of conical part of tent.
Total Surface area of tent = 264 + 770
= 1034 m2
Cloth required = Total Surface area of tent = 1034 m2
Cost of cloth = Rs 80/m2 (given)
Total cost of cloth required = Total surface area of tent × Cost of cloth
= 1034 × Rs. 80
= Rs. 82720
Cost of cloth required to make the tent is Rs. 82720