Surface Area of Cones Quick Check
4 of 5 4 of 5 Items
Question
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
226.08 square feet
226.08 square feet
653.12 square feet
653.12 square feet
113.04 square feet
113.04 square feet
326.56 square feet
To find the surface area of each cone, 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 A = πrℓ, where r is the radius and ℓ is the slant height.
Given that the diameter is 8 feet, the radius is half of that, so r = 4 feet.
So, the lateral surface area of one cone is A = 3.14 * 4 * 5 = 62.8 square feet.
Since there are two cones in the hourglass, the total surface area is 2 * 62.8 = 125.6 square feet.
Therefore, the correct answer is 125.6 square feet.