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.
a. 653.12 square feet
b. 226.08 square feet
c. 326.56 square feet
d. 113.04 square feet
To find the surface area of the cones, we need to find the area of each individual cone and then add them together.
The formula for the lateral surface area of a cone is given by A = πrℓ, where r is the radius of the base and ℓ is the slant height.
The radius is half the diameter, so for each cone, the radius is 8/2 = 4 feet.
The lateral surface area of each cone is A = 3.14 * 4 * 5 = 62.8 square feet.
Since there are two cones, the total surface area of the sculpture is 2 * 62.8 = 125.6 square feet.
Therefore, the correct answer is d. 113.04 square feet.