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)
Responses
113.04 square feet
326.56 square feet
653.12 square feet
226.08 square feet
To find the surface area of each cone, we need to first find the radius using the formula r = d/2 = 8/2 = 4 feet.
Then, we can find the slant height of each cone using the Pythagorean theorem: s = √(r^2 + h^2) = √(4^2 + 5^2) = √(16 + 25) = √41 feet.
The lateral surface area of each cone is given by the formula A = πrs, where r is the radius and s is the slant height. Therefore, the surface area of each cone is A = 3.14 * 4 * √41 = 3.14 * 4 * 6.4 ≈ 80.384 square feet.
Since we have two cones in the sculpture, the total surface area of the outside of the sculpture is 2 * 80.384 = 160.768 square feet.
Therefore, the closest answer is 113.04 square feet, although it is not exact.