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A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m2. |
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Answer» Given, Height of the tent = 77 dm Height of a surmounted cone = 44 dm Height of the Cylindrical Portion = Height of the tent – Height of the surmounted Cone = 77 – 44 = 33 dm = 3.3 m And, given diameter of the cylinder (d) = 36 m So, its radius (r) of the cylinder = 36/2 = 18 m Let’s consider L as the slant height of the cone. Then, we know that L2 = r2 + h2 L2 = 182 + 3.32 L2 = 324 + 10.89 L2 = 334.89 L = 18.3 m Thus, slant height of the cone (L) = 18.3 m Now, the Curved Surface area of the Cylinder (S1) = 2πrh S1 = 2π (184.4) m2 And, the Curved Surface area of the cone (S2) = πrL S2 = π × 18 × 18.3 m2 So, the total curved surface of the tent (S) = S1 + S2 S = S1 + S2 S = (2π18 × 4.4) + (π18 × 18.3) S = 1533.08 m2 Hence, the total Curved Surface Area (S) = 1533.08 m2 Next, The cost of 1 m2 canvas = Rs 3.50 So, 1533.08 m2 of canvas will cost = Rs (3.50 x 1533.08) = Rs 5365.8 |
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