To find the surface area of the outside of the sculpture, we need to find the areas of both cones.
The formula for the surface area of a cone is given by:
\(A = πr (r + l)\)
Where A is the surface area, r is the radius of the cone, and l is the slant height.
Given that the diameter is 8 feet, the radius will be half of that, so r = 8/2 = 4 feet.
Substituting the given values into the formula, we have:
\(A = 3.14 \times 4 (4 + 5)\)
\(A = 3.14 \times 4 \times 9\)
\(A = 113.04 \text{ square feet}\)
Therefore, the designer will need 113.04 square feet of steel for the outside of the sculpture.
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)
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