A designer is creating a modern art sculpture of an hourglass out of steel, to be on display at the town library. Hourglasses made by two cones meeting at the top point. The designer wants to know how many square feet of steel is needed for the outside of the, if the slant height cone is 5 feet and the diameter is 8 feet. Use 3.14 for pi.
1. 226.08 square feet.
2. 113.04 square feet.
3. 326.56 square feet.
4. 653.12 square feet.
To find the surface area of the outside of the hourglass, we need to find the surface area of both cones.
The slant height of the cone is 5 feet, and the diameter is 8 feet. We can use the Pythagorean theorem to find the height of the cone:
height^2 = slant height^2 - radius^2
height^2 = 5^2 - (8/2)^2
height^2 = 25 - 16
height^2 = 9
height = √9
height = 3 feet
The formula for the surface area of a cone is:
surface area = πr(r + slant height)
For the bottom cone:
radius = 8/2 = 4 feet
surface area = 3.14 * 4(4 + 5)
surface area = 3.14 * 4(9)
surface area = 3.14 * 36
surface area = 113.04 square feet
For the top cone:
radius = 0 (since it's converging at the top point)
surface area = πr(r + slant height)
surface area = 3.14 * 0(0 + 5)
surface area = 0 square feet
Therefore, the total surface area of the outside of the hourglass is 113.04 square feet (option 2).