Question

Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2m and height 4m with the conical upper part of the same diameter but height 2.8m and the canvas to be used costs Rs.100 per sqm. Find the amount, the associations will have to pay. What values are shown by the associations?

Answer 1

To find the amount the associations will have to pay, we calculate the total cost of the tents by finding the areas of the cylindrical and conical parts and multiplying them by the cost per square meter of the canvas. The associations will have to pay 2835π Rs. The values shown by the associations include their willingness to contribute and their sense of responsibility.

Step-by-step explanation:

To find the amount the associations will have to pay, we need to calculate the total cost of the tents. Each tent consists of a cylindrical lower part and a conical upper part.

To calculate the area of the cylindrical part, we use the formula for the lateral surface area of a cylinder: 2πrh. In this case, the diameter is 4.2m, so the radius (r) is half of that, or 2.1m. The height (h) of the cylindrical part is 4m. Plugging in these values, we get: 2π(2.1)(4) = 33.6π square meters.

To calculate the area of the conical part, we use the formula for the lateral surface area of a cone: πrl. In this case, the radius (r) is again 2.1m, and the slant height (l) is the hypotenuse of a right-angled triangle with the height (h) and the radius (r) as its legs. Using Pythagoras' theorem, we find that l = sqrt(h^2 + r^2). Plugging in the values, we get: l = sqrt(2.8^2 + 2.1^2) = sqrt(7.84 + 4.41) = sqrt(12.25) = 3.5 meters. Therefore, the area of the conical part is: π(2.1)(3.5) = 23.1π square meters.

The total area of each tent is the sum of the areas of the cylindrical and conical parts: 33.6π + 23.1π = 56.7π square meters. The cost of the canvas is Rs.100 per square meter, so the associations will have to pay: 56.7π * 100 = 5670π Rs. Since the associations are contributing 50% of the cost, their payment will be: 5670π * 0.5 = 2835π Rs.

Therefore, the associations will have to pay 2835π Rs. The values shown by the associations include the willingness to contribute to the cost of the tents and their sense of responsibility in helping those affected by the floods.