To find the surface area of the outside of the sculpture, we need to find the lateral area of each cone and add them together.
The lateral area of a cone is given by the formula L = πrℓ, where r is the radius and ℓ is the slant height.
For the top cone, the radius is half the diameter, so r = 8/2 = 4 feet. The slant height is given as ℓ = 5 feet. Therefore, the lateral area of the top cone is L1 = π(4)(5) = 20π square feet.
For the bottom cone, the radius and slant height are the same as the top cone, so r = 4 feet and ℓ = 5 feet. Therefore, the lateral area of the bottom cone is L2 = π(4)(5) = 20π square feet.
The total surface area of the outside of the sculpture is L1 + L2 = 20π + 20π = 40π square feet.
Approximating π as 3.14, the surface area of the outside of the sculpture is 40(3.14) = 125.6 square feet. Answer: \boxed{125.6}.
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)
1 answer
1 answer