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 113.04 square feet 113.04 square feet 326.56 square feet 326.56 square feet 226.08 square feet 226.08 square feet 653.12 square feet
To find the surface area of the hourglass, we need to find the surface area of both cones and add them together.
The formula for the surface area of a cone is πr(r + l), where r is the radius and l is the slant height.
For the top cone:
Radius = diameter/2 = 8/2 = 4 feet
Slant height = 5 feet
Surface area of top cone = π(4)(4 + 5) = π(4)(9) = 36π square feet
For the bottom cone:
Radius = 8/2 = 4 feet
Slant height = 5 feet
Surface area of bottom cone = π(4)(4 + 5) = π(4)(9) = 36π square feet
Now, add the surface areas of both cones together:
Surface area of hourglass = 36π + 36π = 72π square feet
Approximating π to 3.14,
Surface area of hourglass = 72(3.14) square feet ≈ 226.08 square feet
Therefore, the answer is 226.08 square feet.