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
226.08 square feet
226.08 square feet
326.56 square feet
326.56 square feet
653.12 square feet
653.12 square feet
113.04 square feet
To find the surface area of the hourglass sculpture, we need to calculate the curved surface area of both cones.
First, let's find the slant height of each cone using the Pythagorean theorem:
h = √(r^2 + s^2)
where r is the radius (half the diameter) and s is the slant height.
For both cones, the radius (r) is 8/2 = 4 feet and the slant height (s) is given as 5 feet.
Using the formula:
h = √(4^2 + 5^2)
h = √(16 + 25)
h = √41
h ≈ 6.4 feet
Now, let's find the curved surface area (CSA) of one cone:
CSA = π × r × s
CSA = 3.14 × 4 × 5
CSA = 62.8 square feet (rounded to the nearest tenth)
Since there are two cones in the hourglass, we need to double the CSA to get the total surface area:
Total surface area = 62.8 × 2 = 125.6 square feet
Therefore, the approximate number of square feet of steel needed for the outside of the sculpture is 125.6 square feet.