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.

Answer 1

To calculate the surface area needed for the hourglass sculpture, the lateral surface area of each cone is determined using the formula πrl and then doubled to account for both cones, resulting in 125.6 square feet of steel.

Step-by-step explanation:

The student is tasked with calculating the surface area of a modern art sculpture, which consists of two cones meeting at their vertices to form an hourglass shape. To find the amount of steel needed for the outside of the sculpture, we use the formula for the lateral surface area of a cone, which is πrl, where r is the radius of the base, and l is the slant height. Since the diameter of each cone is 8 feet, the radius r will be half of that, which is 4 feet. The slant height l is given as 5 feet. Substituting these values into the formula, we have:

Surface Area = πrl = 3.14 × 4 ft × 5 ft = 62.8 ft²

Since there are two cones, we need to double the calculated surface area for one cone to cover both cones:

Total Surface Area = 2 × 62.8 ft² = 125.6 ft²

Therefore, the designer will need 125.6 square feet of steel to create the hourglass sculpture.

Answer 2

To find the amount of steel needed for the outside of the sculpture, calculate the surface area of each cone and add them together.

Step-by-step explanation:

To find the amount of steel needed for the outside of the sculpture, we need to calculate the surface area of each cone and then add them together. The formula to find the surface area of a cone is π * r * (r + s), where r is the radius and s is the slant height. First, we need to find the radius by dividing the diameter by 2, so the radius is 8/2 = 4 feet. Then, we can plug the values into the formula: π * 4 * (4 + 5) = 79 square feet.

Since there are two cones, we multiply the surface area of one cone by 2: 79 * 2 = 158 square feet. Therefore, the amount of steel needed for the outside of the sculpture is 158 square feet.