Surface Area of Cones Quick Check

Question

4 of 54 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

113.04 square feet
113.04 square feet

653.12 square feet
653.12 square feet

326.56 square feet
326.56 square feet

226.08 square feet
226.08 square feet

Answer 1

To find the surface area of each cone, we can use the formula:

Surface Area = π * r * (r + l)

First, we need to find the radius. We know the diameter is 8 feet, so the radius is 8/2 = 4 feet.

Next, we need to find the slant height, which is given as 5 feet.

Using these values, we can calculate the surface area of one cone:

Surface Area = 3.14 * 4 * (4 + 5) = 3.14 * 4 * 9 = 113.04 square feet

Since there are two cones in the hourglass, we multiply this by 2 to find the total surface area:

Total Surface Area = 113.04 * 2 = 226.08 square feet

Therefore, the correct answer is:

226.08 square feet