The slant height is 22 and the diameter is 25. What is the surface area of the cone? Use 3.14 for pi.
A) 863. 5 square centimeters
B) 1, 354.125 square centimeters
C) 2, 383.26 square centimeters
D) 3,689.5 sqaure centimeters
The surface area of a cone can be calculated using the formula:
Surface Area = πr^2 + πrL
Where r is the radius of the base and L is the slant height.
Since the diameter is given as 25, the radius would be half of that, which is 25/2 = 12.5.
Using the given slant height of 22, we can calculate the surface area by substituting the values into the formula.
Surface Area = π(12.5)^2 + π(12.5)(22)
Surface Area = 3.14(156.25) + 3.14(275)
Surface Area ≈ 490.625 + 863.5
Surface Area ≈ 1354.125
Therefore, the surface area of the cone is approximately 1354.125 square centimeters.
The correct answer is B) 1, 354.125 square centimeters.
A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 pi.
A) 339.12 square centimeters
B) 452.17 square centimeters
C) 197.82 square centimeters
D) 1,356.48 square centimeters
The surface area of a cone can be calculated using the formula:
Surface Area = πr^2 + πrL
Where r is the radius of the base and L is the slant height.
In this case, the radius is given as 6 centimeters, and the slant height is given as 18 centimeters.
Substituting these values into the formula:
Surface Area = π(6)^2 + π(6)(18)
Surface Area = 3.14(36) + 3.14(108)
Surface Area ≈ 113.04 + 339.12
Surface Area ≈ 452.16
Therefore, the surface area of the spyglass is approximately 452.16 square centimeters.
The correct answer is B) 452.17 square centimeters.
A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 pi.
A) 339.12 square centimeters
B) 452.16 square centimeters
C) 197.82 square centimeters
D) 1,356.48 square centimeters
The surface area of the spyglass can be calculated using the formula for the surface area of a cone:
Surface Area = πr^2 + πrL
Where r is the radius of the base and L is the slant height.
Given that the radius is 6 centimeters and the slant height is 18 centimeters, we can substitute these values into the formula:
Surface Area = 3.14 * (6)^2 + 3.14 * 6 * 18
Surface Area = 3.14 * 36 + 3.14 * 108
Surface Area = 113.04 + 339.12
Surface Area = 452.16
Therefore, the surface area of the spyglass is approximately 452.16 square centimeters.
The correct answer is B) 452.16 square centimeters.
A designer is creating a model 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 start height of each cone is 5 feet and the diameter is 8 feet. Use 3.14 pi.
A) 113.04 square feet
B) 653.12 square feet
C) 226.08 square feet
D) 326.56 square feet
To find the surface area of the hourglass sculpture, we need to find the area of each cone separately and then add them together.
First Cone:
Radius = Diameter/2 = 8/2 = 4 feet
Slant Height = Height = 5 feet
The surface area of the first cone can be calculated as:
Surface Area = πr^2 + πrL
Surface Area = 3.14 * (4)^2 + 3.14 * 4 * 5
Surface Area = 3.14 * 16 + 3.14 * 20
Surface Area = 50.24 + 62.8
Surface Area = 113.04 square feet
Second Cone:
Radius = Diameter/2 = 8/2 = 4 feet
Slant Height = Height = 5 feet (since it has the same dimensions as the first cone)
The surface area of the second cone can be calculated in the same way:
Surface Area = πr^2 + πrL
Surface Area = 3.14 * (4)^2 + 3.14 * 4 * 5
Surface Area = 3.14 * 16 + 3.14 * 20
Surface Area = 50.24 + 62.8
Surface Area = 113.04 square feet
To find the total surface area of the hourglass sculpture, we need to add the surface areas of both cones:
Total Surface Area = 113.04 + 113.04
Total Surface Area = 226.08 square feet
Therefore, the designer will need 226.08 square feet of steel for the outside of the sculpture.
The correct answer is C) 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?
A) 10.9 square centimeters
B) 1, 884 square centimeters
C) 942 square centimeters
D) 1, 648.5 square centimeters
The lateral surface area of a cone can be calculated using the formula:
Lateral Surface Area = πrL
Where r is the radius of the base and L is the slant height.
Given that the radius is 15 centimeters and the slant height is 20 centimeters, we can substitute these values into the formula:
Lateral Surface Area = 3.14 * 15 * 20
Lateral Surface Area = 942 square centimeters
Therefore, the lateral surface area of the megaphone is 942 square centimeters.
The correct answer is C) 942 square centimeters.