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Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively decided to provide place and the canvas for 1500 tents and share the whole expenditure equally. The lower part of each tent is cylindrical with base radius 2.8 m and height 3.5 m and the upper part is conical with the same base radius, but of height 2.1 m. If the canvas used to make the tents costs β‚Ή120 per m 2 , find the amount shared by each school to set up the tents

 

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Question 34 (Choice 1) Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively decided to provide place and the canvas for 1500 tents and share the whole expenditure equally. The lower part of each tent is cylindrical with base radius 2.8 m and height 3.5 m and the upper part is conical with the same base radius, but of height 2.1 m. If the canvas used to make the tents costs β‚Ή120 per m2 , find the amount shared by each school to set up the tentsWe need to find amount shared by each school to set up the tents Amount Shared = (π‘‡π‘œπ‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘šπ‘Žπ‘˜π‘–π‘›π‘” 1500 𝑑𝑒𝑛𝑑𝑠)/(π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘†π‘β„Žπ‘œπ‘œπ‘™π‘ ) = (1500 Γ— π‘‡π‘œπ‘‘π‘Žπ‘™ πΆπ‘œπ‘ π‘‘ π‘œπ‘“ π‘šπ‘Žπ‘˜π‘–π‘›π‘” 1 𝑑𝑒𝑛𝑑)/50 = 30 Γ— Total cost of making 1 tent Now, Total cost of making 1 tent = Rate Γ— Area of material required = 120 Γ— (CSA of cone + CSA of cylinder)Curved Surface Area of Cone Radius of cone = 2.8 cm Height of cone = 2.1 cm We need to find slant height l l = √(π‘Ÿ^2+β„Ž^2 ) l = √(γ€–(2.8)γ€—^2 + γ€–(2.1)γ€—^2 ) l = √(((4 Γ— 7)/10)^2+((3 Γ— 7)/10)^2 ) l = √((7/10)^2 [4^2+3^2 ] ) l = 7/10 √((16+9)) l = 7/10 √25 l = 7/10 Γ— 5 l = 3.5 m l = 7/10 Γ— 5 l = 3.5 m Now, Curved Surface area of cone = πœ‹π‘Ÿπ‘™ = πœ‹ Γ— 2.8 Γ— 3.5 = 22/7Γ—28/10 Γ—35/10 = 22 Γ—4/10 Γ—35/10 = 30.8 m2Curved Surface Area of Cylinder Radius of cylinder = 2.8 cm Height of cylinder = 3.5 cm Now, Curved Surface area of cylinder = 2πœ‹π‘Ÿβ„Ž = 2 Γ— πœ‹ Γ— 2.8 Γ— 3.5 = 2 Γ— 22/7Γ—28/10 Γ—35/10 = 2 Γ— 22 Γ—4/10 Γ—35/10 = 61.6 m2 Now, Total cost of making 1 tent = 120 Γ— (CSA of cone + CSA of cylinder) = 120 Γ— (61.6 + 30.8) = 120 Γ— 92.4 = Rs 11,088 Therefore, Amount Shared = 30 Γ— Total cost of making 1 tent = 30 Γ— 11088 = Rs 3,32,640

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.