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A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5m.(i) How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground?(ii) Find the volume of the cone. |
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Answer» (i) We know that Area of the floor of the tent = πr2 By substituting the values Area of the floor of the tent = (22/7) × 52 = 550/7 m2 We know that the area required by one student is 5/7 m2 So the required number of students = (550/7)/ (5/7) = 110 (ii) We know that Curved surface area of the tent = area of the cloth = 165 m2 So we get πrl = 165 By substituting the values (22/7) × 5 × l = 165 On further calculation l = (165 × 7)/ (22 × 5) = 21/2 m We know that h = √ (l2 – r2) By substituting the values h = √ ((21/2)2 – 52) On further calculation h = √ ((441/4) – 25) = √ (341/4) So we get h = 9.23 m We know that Volume of the tent = 1/3 πr2h By substituting the values Volume of the tent = 1/3 × (22/7) × 52 × 9.23 On further calculation Volume of the tent = 241.7 m3 |
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