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
113.04 square feet
113.04 square feet
326.56 square feet
326.56 square feet
653.12 square feet
653.12 square feet
226.08 square feet
To calculate the surface area of each cone, we will first find the slant height of the cone using the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle formed by the slant height (5 feet), the radius (4 feet), and the height of the cone (h).
Using the Pythagorean theorem, we can find the height (h) of each cone as follows:
l² = h² + r²
5² = h² + 4²
25 = h² + 16
h² = 9
h = √9
h = 3 feet
Now, we can calculate the surface area of each cone using the formula:
A = πr(r + l)
For the first cone:
Radius (r) = 4 feet
Slant height (l) = 5 feet
A₁ = π * 4(4 + 5)
A₁ = 3.14(4)(9)
A₁ = 113.04 square feet
For the second cone, we have the same values for r and l, so the surface area is also 113.04 square feet.
Therefore, the total surface area of the outside of the sculpture is 113.04 + 113.04 = 226.08 square feet.
The correct answer is 226.08 square feet.