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?(See the formula sheets - Recall that the LATERAL (sides only-not bottom) surface area of a cone= pi r s where s is the slant height)
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?(See the formula sheets - Recall that the LATERAL (sides only-not bottom) surface area of a cone= pi r s where s is the slant height)
Solution
To solve this problem, we need to follow these steps:
-
Calculate the lateral surface area of the cone using the formula: pi * r * s. Here, r is the radius (3 ft) and s is the slant height (5 ft).
-
Convert the surface area from square feet to square yards because the canvas is sold by the square yard. There are 9 square feet in a square yard, so divide the surface area by 9.
-
Multiply the surface area in square yards by the cost per square yard to find the total cost of the material.
Let's do the calculations:
-
Surface area = pi * r * s = 3.14159 * 3 ft * 5 ft = 47.12385 square feet.
-
Surface area in square yards = 47.12385 square feet / 9 = 5.236094 square yards.
-
Total cost = 5.236094 square yards * 120.43.
So, the material for the tent will cost approximately $120.43.
Similar Questions
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.
Monica has a piece of canvas whose area is 551 m². She uses it tohave a conical tent made, with a base radius of 7 m. Assuming that allthe stitching margins and the wastage incurred while cutting, amountsto approximately 1 m²(i)Find the slant height of the conical tent so formed.(ii)Find the height of the conical tent so formed.(iii) find the volume of the conical tent?
Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)$
find the length of cloth, 2m in width, required to make a conical tent having diameter 12m and slant height 12.6m
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.