A party planner is designing a conical canvas tent for a child's birthday party. The tent has no floor, and it has a radius of 3 ft, a perpendicular height of 4 ft, and a slant height of 5 ft. If canvas sells by the square yard only, for $23.00/yd2, how much will the material cost?
Question
A party planner is designing a conical canvas tent for a child's birthday party. The tent has no floor, and it has a radius of 3 ft, a perpendicular height of 4 ft, and a slant height of 5 ft. If canvas sells by the square yard only, for $23.00/yd2, how much will the material cost?
Solution
To solve this problem, we need to find the surface area of the conical tent and then convert that area into square yards to find the cost of the canvas.
Step 1: Find the surface area of the conical tent. The formula for the surface area of a cone is πr(r + l), where r is the radius and l is the slant height.
Substituting the given values, we get:
Surface area = π * 3 * (3 + 5) = 24π square feet.
Step 2: Convert the surface area from square feet to square yards. There are 9 square feet in a square yard, so we divide the surface area by 9.
24π / 9 = 8π/3 square yards.
Step 3: Multiply the surface area in square yards by the cost per square yard to find the total cost.
Total cost = 8π/3 * 192π/3 ≈ $200.96.
So, the material for the tent will cost approximately $200.96.
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