A tent is cylindrical up to a height of 2.1 m and conical above it. If the diameter of the base is 2.6 m and the slant height of the conical part is 3.5 m, find the total canvas used in making the tent.
Question
A tent is cylindrical up to a height of 2.1 m and conical above it. If the diameter of the base is 2.6 m and the slant height of the conical part is 3.5 m, find the total canvas used in making the tent.
Solution
To solve this problem, we need to find the surface area of both the cylindrical and conical parts of the tent.
Step 1: Find the radius of the base The diameter of the base is given as 2.6 m. The radius is half of the diameter, so the radius (r) is 2.6 m / 2 = 1.3 m.
Step 2: Find the surface area of the cylindrical part The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. Here, r = 1.3 m and h = 2.1 m. So, the surface area of the cylindrical part is 2 * π * 1.3 m * 2.1 m = 8.6454 m².
Step 3: Find the surface area of the conical part The formula for the lateral surface area of a cone is πrl, where r is the radius and l is the slant height. Here, r = 1.3 m and l = 3.5 m. So, the surface area of the conical part is π * 1.3 m * 3.5 m = 14.323 m².
Step 4: Find the total surface area of the tent The total surface area of the tent is the sum of the surface areas of the cylindrical and conical parts. So, the total canvas used in making the tent is 8.6454 m² + 14.323 m² = 22.9684 m².
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