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
To find the surface area of each cone, we need to find the area of the base and the lateral surface area.
The radius of each cone is half the diameter, so r = 8 / 2 = 4 feet.
1. Area of the base of each cone = π * r^2 = 3.14 * 4^2 = 3.14 * 16 = 50.24 square feet.
2. Lateral surface area of each cone = π * r * slant height = 3.14 * 4 * 5 = 62.8 square feet.
Since there are two cones, the total surface area of the hourglass sculpture is 2 * (base area + lateral surface area) = 2 * (50.24 + 62.8) = 2 * 113.04 = 226.08 square feet.
Therefore, the designer needs 226.08 square feet of steel for the outside of the sculpture.