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)
113.04 square feet
O326.56 square feet
O226.08 square feet
O 653.12 square feet
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)
O326.56 square feet
O226.08 square feet
O 653.12 square feet
To solve this problem, we need to calculate the surface area of each cone and then add them together.
First, let's calculate the surface area of a cone. The formula for the surface area of a cone is given by:
Surface Area = π * r * (r + l)
Where:
π = 3.14
r = radius of the base of the cone
l = slant height of the cone
In this case, the diameter of the cone is given as 8 feet, so the radius would be half of that, which is 8/2 = 4 feet. The slant height is given as 5 feet.
For the first cone, the surface area would be:
Surface Area of first cone = 3.14 * 4 * (4 + 5)
Next, let's calculate the surface area of the second cone. Since it is identical to the first cone, the surface area would be the same:
Surface Area of second cone = 3.14 * 4 * (4 + 5)
Now, we can add the surface areas of the two cones together to find the total surface area of the sculpture:
Total surface area = Surface Area of first cone + Surface Area of second cone
Once you calculate this, you will find that the correct answer is O 226.08 square feet.
To find the surface area of the two cones, we need to find the lateral area of each cone and then add them together.
The lateral area of a cone can be found using the formula: πrs, where r is the radius of the base and s is the slant height.
Given that the diameter is 8 feet, the radius is half of that, which is 4 feet.
For the first cone:
Lateral area = π(4)(5) = 20π square feet
For the second cone:
Lateral area = π(4)(5) = 20π square feet
Adding both lateral areas:
20π + 20π = 40π square feet
Approximating π as 3.14:
40(3.14) = 125.6 square feet
Therefore, the amount of steel needed for the outside of the sculpture is approximately 125.6 square feet.
The closest answer choice is 113.04 square feet.
To find the surface area of the two cones, we need to find the lateral area of each cone and then add them together.
The lateral area of a cone can be found using the formula: πrs, where r is the radius of the base and s is the slant height.
Given that the diameter is 8 feet, the radius is half of that, which is 4 feet.
For the first cone:
Lateral area = π(4)(5) = 20π square feet
For the second cone:
Lateral area = π(4)(5) = 20π square feet
Adding both lateral areas:
20π + 20π = 40π square feet
Approximating π as 3.14:
40(3.14) = 125.6 square feet
Therefore, the amount of steel needed for the outside of the sculpture is approximately 125.6 square feet.
The closest answer choice is O326.56 square feet.