Question: Due to heavy floods in a state, thousand were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs 120 per sq.m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (use = π \\frac{22}{7}))
Video Explanation
Explanatory Answer
Number of tents = 1500
Shape of tent: cylindrical base and conical top
Dimension of cylinder: Base radius 2.8m, height 3.5m
Dimension of cone: Base radius 2.8m, height 2.1m
Number of schools participating in the program = 50
Cost of canvas used to make test = Rs.120/m2
Area of canvas for 1 tent = Lateral surface area of cylinder + Lateral surface area of cone.
Lateral surface area of cylinder = 2πrh
= 2 × \\frac{22}{7}) × 2.8 × 3.5
= 61.6 sq m
Lateral Surface area of cone = πrl, where l is the slant height of the cone.
Slant height l = \\sqrt {r^2 + h^2}) = \\sqrt{2.8^2 + 2.1^2})
= \\sqrt{{(0.7 × 4)^2} + {(0.7 × 3)^2}}) = 0.7\\sqrt{4^2 + 3^2})
= 0.7 \\sqrt{25}) = 0.7 × 5 = 3.5m
Lateral surface area the cone = \\frac{22}{7}) × 2.8 × 3.5 = 30.8 sqm
Area of canvas for 1 tent = 61.6 + 30.8 = 92.4 sqm
Total area of canvas for 1500 tents = 1500 × 92.4 sqm
Total cost of canvas = Total area of cavas × cost per sq m = 1500 × 92.4 × 120
Amount shared by each school = \\frac{1500 × 92.4 × 120}{50}) (Note: Keep the calculation to the last step. 50 will divide 1500 and make calculations easy.)
= 30 × 92.4 × 120
= Rs. 3,32,640