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
326.56 square feet
326.56 square feet
113.04 square feet
113.04 square feet
226.08 square feet
226.08 square feet
653.12 square feet
To find the surface area of the outside of the sculpture, we need to find the area of both cones and sum them up.
First, let's find the radius of the cones. The diameter is given as 8 feet, so the radius is half of that, which is 4 feet.
Next, let's find the slant height of the cones. It is given as 5 feet.
To find the lateral surface area of a cone, we use the formula: π * radius * slant height.
For each cone, the lateral surface area is:
π * 4 feet * 5 feet = 20π square feet.
Now, we need to find the total surface area by summing up the areas of both cones:
20π square feet + 20π square feet = 40π square feet.
Finally, let's approximate the value of pi using 3.14:
40π square feet ≈ 40 * 3.14 square feet ≈ 125.6 square feet.
Therefore, the correct answer is 125.6 square feet, which is closest to the second option, 113.04 square feet.