To find the total surface area of the outside of the sculpture, we need to find the lateral surface area of each cone and then add them together.
The lateral surface area of a cone is given by the formula: πr*s, where r is the radius of the base of the cone and s is the slant height.
For each cone:
Radius = diameter/2 = 8/2 = 4 feet
Slant height = 5 feet
Lateral surface area of one cone = π*4*5 = 20π square feet
Since there are two cones in the sculpture, the total surface area is:
Total surface area = 2*(20π) = 40π square feet
Approximating π to 3.14:
Total surface area ≈ 40*3.14 = 125.6 square feet
Therefore, the designer needs approximately 125.6 square feet of steel for the outside of the sculpture.
The closest option provided is 113.04 square feet.
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 653.12 square feet 653.12 square feet 326.56 square feet 326.56 square feet 113.04 square feet 113.04 square feet 226.08 square feet
1 answer