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
226.08 square feet
226.08 square feet
113.04 square feet
113.04 square feet
653.12 square feet
653.12 square feet
326.56 square feet
To find the surface area of the hourglass, we need to calculate the surface area of both cones and add them together.
The formula for the surface area of a cone is given by: π * r * l + π * r^2, where r is the radius and l is the slant height.
For the first cone, the radius is half of the diameter, so it is 8/2 = 4.
Surface area of the first cone = π * 4 * 5 + π * 4^2
= 20π + 16π
= 36π
For the second cone, the dimensions are the same, so the surface area is also 36π.
Now, we add the surface areas of both cones together:
36π + 36π = 72π
To find the surface area in square feet, we need to multiply by π ≈ 3.14:
72π * 3.14 = 226.08 square feet
Therefore, the correct answer is:
226.08 square feet
A cone-shaped megaphone has a radius of 15 centimeters and a slant height of 20 centimeters. A megaphone has an open bottom. What is the lateral surface area of the megaphone, in square centimeters? Use 3.14 for pi.(1 point)
Responses
1,648.5 square centimeters
1,648.5 square centimeters
1,884 square centimeters
1,884 square centimeters
942 square centimeters
942 square centimeters
109.9 square centimeters