To determine the surface area of the hourglass sculpture, we need to calculate the lateral surface area of each cone and then add them together.
First, let's find the slant height (l) of each cone. Given the diameter (d) of each cone, we can use the Pythagorean theorem:
l² = h² + r²
where h is the height and r is the radius of the cone.
Since the diameter (d) is 8 feet, the radius (r) is half of that, which is 4 feet.
Using the formula above, we can calculate the slant height (l) as follows:
l² = h² + 4²
l² = h² + 16
We are given that the slant height (l) is 5 feet, so we can substitute that into the equation:
5² = h² + 16
25 = h² + 16
h² = 25 - 16
h² = 9
h = √9
h = 3 feet
Now that we have the height (h) and the radius (r), we can calculate the lateral surface area of each cone using the formula:
Lateral surface area = π * r * l
For the first cone, the radius (r) is 4 feet and the slant height (l) is 5 feet:
Lateral surface area of the first cone = 3.144 * 4 * 5 = 62.88 square feet
For the second cone, the radius (r) is also 4 feet and the slant height (l) is also 5 feet:
Lateral surface area of the second cone = 3.144 * 4 * 5 = 62.88 square feet
Since the hourglass is formed by two cones meeting at the top point, we need to add the lateral surface areas of both cones together:
Total surface area = 62.88 + 62.88 = 125.76 square feet
Therefore, the outside of the hourglass sculpture requires approximately 125.76 square feet of steel.
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 structure if the slant height of each cone is 5 feet and the diameter is 8 feet use 3.144 pi
1 answer
1 answer