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
To calculate the surface area of each cone, we need to find the slant height and the base radius.
Given:
Diameter of the cone = 8 feet
Radius of the cone (r) = Diameter / 2 = 8 / 2 = 4 feet
Slant height (l) = 5 feet
Now, we can use the formula for the surface area of a cone:
Surface Area of a Cone = π * r * l
For the first cone:
Surface Area of the first cone = π * 4 * 5 ≈ 62.8 square feet
Since there are two cones in the hourglass sculpture, we need to multiply the surface area of one cone by 2 to account for both cones.
Total surface area of the two cones = 62.8 * 2 = 125.6 square feet
Therefore, the designer will need approximately 125.6 square feet of steel for the outside of the sculpture.