A designer is creating a modern art sculpture of an hourglass out of steel to be on display at the town brary The hourglass made by bec 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 at eg of each cone is 5 feet and the diameter is 8 feet Use 3 14 for p (1 point)
653.12 square feet
113.04 square feet
O225.08 square feet
326 56 square feet
To find the surface area of the outside of the hourglass sculpture, we'll first find the slant height of each cone:
Using the Pythagorean theorem, with the radius (diameter/2) as one leg and the height as the other leg:
r = 8/2 = 4 feet
h = 5 feet
Applying the Pythagorean theorem:
slant height = √(4^2 + 5^2) = √(16 + 25) = √41
Now, we can find the surface area of each cone using the formula:
SA = πr(r + slant height)
For each cone:
SA = π(4)(4 + √41)
Finally, adding the surface area of both cones together:
Total surface area = 2 x SA = 2π(4)(4 + √41)
Using the value of π as approximately 3.14:
Total surface area = 2(3.14)(4)(4 + √41)
Total surface area ≈ 653.12 square feet
Therefore, the correct answer is 653.12 square feet.