Surface Area of Cones Quick Check
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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.(1 point)
Responses
653.12 square feet
653.12 square feet
113.04 square feet
113.04 square feet
326.56 square feet
326.56 square feet
226.08 square feet
226.08 square feet
To find the surface area of the cones, we first need to find the slant height of the cones. We can use the Pythagorean theorem to find the slant height:
l^2 = r^2 + h^2
5^2 = 4^2 + h^2
25 = 16 + h^2
h^2 = 9
h = 3
So the slant height (l) of each cone is 5 feet and the radius (r) is half of the diameter, so r = 4 feet.
The surface area of a cone is given by the formula:
A = πrl + πr^2
For one cone:
A = 3.14*4*5 + 3.14*4^2
A = 62.8 + 50.24
A = 113.04 square feet
The total surface area of steel needed for the entire sculpture is double that:
Total surface area = 2 * 113.04
Total surface area = 226.08 square feet
Therefore, the correct answer is 226.08 square feet.