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. 326.56
2. 653.12
3. 113.04
4. 226.08
To find the surface area of the outside of the sculpture, we need to calculate the surface area of each cone and add them together.
The surface area of a cone is given by the formula: A = πrℓ, where A is the surface area, π is approximately 3.14, r is the radius, and ℓ is the slant height.
For each cone, the radius is half of the diameter, so r = 8/2 = 4 feet.
For each cone, the slant height is given as 5 feet.
Let's calculate the surface area of one cone:
A = π * 4 * 5
A = 62.8 square feet
Since there are two cones, the total surface area is 2 * 62.8 = 125.6 square feet.
So the amount of steel needed for the outside of the sculpture is 125.6 square feet.
Answer: 125.6 square feet.