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 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.
choose one
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.
To find the total surface area of the hourglass sculpture, we need to calculate the surface area of each cone and then add them together.
The formula to calculate the surface area of a cone is:
Surface Area = π × r × (r + slant height), where r is the radius and slant height is the slanted side of the cone.
First, we need to find the radius of the cone. Since the diameter is given as 8 feet, we can divide it by 2 to find the radius:
Radius = Diameter / 2 = 8 ft / 2 = 4 ft.
Next, we need to find the surface area of one of the cones. Plugging the values into the formula:
Surface Area of Cone = 3.14 × 4 ft × (4 ft + 5 ft)
Surface Area of Cone = 3.14 × 4 ft × 9 ft
Surface Area of Cone = 113.04 square feet (approximately)
Since there are two cones in the hourglass sculpture, we need to double the surface area of one cone to find the total surface area of the hourglass.
Total Surface Area = 2 × 113.04 square feet
Total Surface Area = 226.08 square feet
Therefore, the answer is 226.08 square feet.