A designer is creating a modern art sculpture of an hourglass out of steel to be displayed 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 ft in the demeanor is 8 ft you use 3.14 for pi
To find the surface area of the hourglass sculpture, we need to calculate the surface area of each cone and then add them together.
The formula for the surface area of a cone is:
A = πr(r + l)
where A is the surface area, r is the radius, and l is the slant height.
First, let's calculate the radius of each cone. The diameter is given as 8 ft, so the radius is half of that, which is 8/2 = 4 ft.
Now, let's calculate the surface area of each cone:
Surface area of first cone = π(4)(4 + 5) = 3.14(4)(9) = 113.04 square feet
Surface area of second cone = π(4)(4 + 5) = 3.14(4)(9) = 113.04 square feet
Finally, we add the surface areas of the two cones together to get the total surface area of the hourglass sculpture:
Total surface area = 113.04 + 113.04 = 226.08 square feet
Therefore, the designer will need 226.08 square feet of steel for the outside of the sculpture.