Final answer:
To find the area of the canvas used in making the tent, you need to calculate the lateral surface area of the cylindrical part and the curved surface area of the conical top, and then add them together. The total area of the canvas used in making the tent is 2905.36 m².
Step-by-step explanation:
To find the area of the canvas used in making the tent, we need to calculate the lateral surface area of the cylindrical part and the curved surface area of the conical top and then add them together.
Let's break it down step by step:
1. Calculating the lateral surface area of the cylindrical part:
Lateral surface area of a cylinder = 2 * π * radius * height
Given that the common diameter is 56 m and the height of the cylindrical part is 6 m, the radius of the cylinder will be half of the diameter, i.e., 28 m.
Plugging the values into the formula:
Lateral surface area of the cylindrical part = 2 * 3.14 * 28 * 6 = 1055.68 m²
2. Calculating the curved surface area of the conical top:
Curved surface area of a cone = π * radius * slant height
Since the diameter of the cylindrical part is equal to the diameter of the conical top, the radius of the conical top will also be 28 m. Now, we need to find the slant height of the conical top. The total height of the tent above the ground is given as 27 m, and the height of the cylindrical part is 6 m. So, the slant height of the conical top will be 27 - 6 = 21 m. Substituting the values into the formula:
Curved surface area of the conical top = 3.14 * 28 * 21 = 1849.68 m²
3. Adding the two areas together:
Total area of the canvas used = Lateral surface area of the cylindrical part + Curved surface area of the conical top
Total area = 1055.68 + 1849.68 = 2905.36 m²