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)

Question

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

Answer 1

To calculate the surface area of each cone, we need to find the slant height, radius, and the lateral surface area using the formula:

Lateral Surface Area of a Cone = π * r * l

Given that the diameter is 8 feet, we can calculate the radius by dividing it by 2:

Radius = diameter / 2 = 8 ft / 2 = 4 ft

And the slant height is given as 5 feet.

Now, we can calculate the lateral surface area of each cone:

Lateral Surface Area = π * 4 ft * 5 ft = 20π ft²

Since we have two cones, we need to multiply this value by 2:

Total Surface Area = 2 * 20π ft²

Using the value of pi as 3.14, we can approximate the total surface area:

Total Surface Area ≈ 2 * 20 * 3.14 ft²

Total Surface Area ≈ 125.6 ft²

Therefore, the designer will need approximately 125.6 square feet of steel for the outside of the sculpture.

None of the given responses match this calculation, so none of them are correct.

Answer 2

choose one

Answer 3

If I have to choose one option from the given responses, I would go with 326.56 square feet. However, this answer is not correct based on the calculation provided.