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 find the surface area of each cone, we need to find the lateral area and then multiply by 2 (since there are two cones).
The lateral area of a cone can be found by multiplying pi times the radius times the slant height. Notice that the radius is half of the diameter, so R = 8 ft / 2 = 4 ft.
The lateral area of each cone is then (3.14)(4 ft)(5 ft) = 62.8 square feet.
The total surface area of both cones is 2 * 62.8 square feet = 125.6 square feet.
Therefore, the designer needs 125.6 square feet of steel for the outside of the sculpture.