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?

Answer 1

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

We are given

$$r = 3 \, \text{ft}$$ $$l = 5 \, \text{ft}$$ $$h = 4 \, \text{ft}$$

According to Wikipedia http://en.wikipedia.org/wiki/Cone_(geometry)#Surface_Area

The lateral surface of a cone is:

$$SA = \pi r l$$

Calculating

$$SA = 3.14 * 3 * 5 = 47.1 \, \text{ft}^2$$

So we need 47.1 ft² of material to make the conical tent without floor.

Converting ft² into yd²

$$1 \, \text{yd} = 3 \, \text{feet}$$ $$1 \, \text{feet} = \frac{1}{3} \, \text{yd}$$ $$1 \, \text{ft}^2 = \frac{1}{9} \, \text{yd}^2$$

Thus:

$$SA = 47.1 \, \text{ft}^2 = \frac{47.1}{9} \, \text{yd}^2 = 5.233 \, \text{yd}^2$$

As canvas sells by the square yard only we should by 6 yd² of it.

It will cost:

$$6 * 23 = \$138$$

Answer:

$$\$138$$