A designer is creating a modern art sculpture of an hourglass out of steel, to be on display at the town library. The hourglass is 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 sculpture, if the slant height of each cone is 5 feet and the diameter is 8 feet. Use 3.14 for pi. (1 point)
326.56 square feet
653.12 square feet
226.08 square feet
113.04 square feet
To find the surface area of each cone, we need to find the lateral area of a cone and then multiply it by 2 since there are two cones in the sculpture.
The lateral area of a cone can be found using the formula:
Lateral Area = π * r * s
Where r is the radius of the base (half of the diameter) and s is the slant height.
For each cone, the radius is 8/2 = 4 feet and the slant height is 5 feet.
Lateral Area of each cone = 3.14 * 4 * 5 = 62.8 square feet
And since there are two cones:
Total lateral area of the two cones = 2 * 62.8 = 125.6 square feet
Therefore, the designer will need 125.6 square feet of steel for the outside of the sculpture. However, this is only the lateral area of the cones and does not include the bases of the cones.
To find the area of the base of each cone, we use the formula for the area of a circle:
Base Area = π * r^2
Where r is the radius of the base.
For each cone, the radius is 8/2 = 4 feet.
Base Area of each cone = 3.14 * 4^2 = 3.14 * 16 = 50.24 square feet
And since there are two bases:
Total base area of the two cones = 2 * 50.24 = 100.48 square feet
Adding the lateral area and base area together:
Total surface area = 125.6 + 100.48 = 226.08 square feet.
Therefore, the designer will need 226.08 square feet of steel for the outside of the sculpture.
Answer: 226.08 square feet