Question
What is the surface area, in square inches, of a cone with a radius of 10 inches and a slant height of 15 inches? Use 3.14 for pi.(1 point)
Responses
471 square inches
471 square inches
1,177.5 square inches
1,177.5 square inches
2,198 square inches
2,198 square inches
785 square inches
To find the surface area of a cone, we need to find the lateral surface area and add it to the base area.
The lateral surface area of a cone can be found using the formula: LSA = π * radius * slant height.
Given that the radius is 10 inches and the slant height is 15 inches, we can calculate the lateral surface area:
LSA = 3.14 * 10 * 15 = 471 square inches.
The base area of a cone can be found using the formula: base area = π * radius^2.
Given that the radius is 10 inches, we can calculate the base area:
base area = 3.14 * 10^2 = 314 square inches.
Now, we can find the total surface area by adding the lateral surface area and the base area:
total surface area = lateral surface area + base area = 471 + 314 = 785 square inches.
The correct answer is 785 square inches.
Use the image to answer the question.
A cone shows a base diameter of 25 centimeters, perpendicular height from the base to the top vertex at 90 degrees, and 22 centimeters as the hypotenuse or the side of the cone.
What is the surface area of the cone? Use 3.14 for pi.
(1 point)
Responses
863.5 square centimeters
863.5 square centimeters
1,354.125 square centimeters
1,354.125 square centimeters
2,383.26 square centimeters
2,383.26 square centimeters
3,689.5 square centimeters
To find the surface area of a cone, we need to find the lateral surface area and add it to the base area. The lateral surface area of a cone can be found using the formula: LSA = π * radius * slant height.
Given that the diameter of the base is 25 centimeters, the radius would be half of that, which is 12.5 centimeters. The slant height is given as 22 centimeters.
Using these values, we can calculate the lateral surface area:
LSA = 3.14 * 12.5 * 22 = 865.5 square centimeters.
Next, we need to find the base area of the cone. The base area can be found using the formula: base area = π * radius^2.
Given that the radius is 12.5 centimeters, we can calculate the base area:
Base area = 3.14 * 12.5^2 = 490.625 square centimeters.
Now, we can find the total surface area by adding the lateral surface area and the base area:
Total surface area = lateral surface area + base area = 865.5 + 490.625 = 1,356.125 square centimeters.
The correct answer is 1,356.125 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 for pi.(1 point)
Responses
197.82 square centimeters
197.82 square centimeters
1,356.48 square centimeters
1,356.48 square centimeters
452.16 square centimeters
452.16 square centimeters
339.12 square centimeters
To find the surface area of a cone, we need to find the lateral surface area and add it to the base area.
The lateral surface area of a cone can be found using the formula: LSA = π * radius * slant height.
Given that the radius is 6 centimeters and the slant height is 18 centimeters, we can calculate the lateral surface area:
LSA = 3.14 * 6 * 18 = 339.12 square centimeters.
Next, we need to find the base area of the cone. The base area can be found using the formula: base area = π * radius^2.
Given that the radius is 6 centimeters, we can calculate the base area:
Base area = 3.14 * 6^2 = 113.04 square centimeters.
Now, we can find the total surface area by adding the lateral surface area and the base area:
Total surface area = lateral surface area + base area = 339.12 + 113.04 = 452.16 square centimeters.
The correct answer is 452.16 square centimeters.
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
113.04 square feet
113.04 square feet
226.08 square feet
226.08 square feet
326.56 square feet
326.56 square feet
653.12 square feet
To find the surface area of the hourglass sculpture, we need to find the sum of the surface areas of the two cones.
The surface area of a cone can be found by adding the lateral surface area and the base area.
First, let's calculate the surface area of one cone.
The slant height of each cone is given as 5 feet, and the diameter of the base is 8 feet.
The radius of the cone can be found by dividing the diameter by 2: radius = 8 ft / 2 = 4 ft.
The lateral surface area of the cone can be found using the formula: LSA = π * radius * slant height.
For one cone:
LSA = 3.14 * 4 * 5 = 62.8 square feet.
The base area of the cone can be found using the formula: base area = π * radius^2.
For one cone:
Base area = 3.14 * 4^2 = 50.24 square feet.
Now, let's find the total surface area by summing the surface areas of the two cones:
Total surface area = 2 * (lateral surface area + base area) = 2 * (62.8 + 50.24) = 2 * 113.04 = 226.08 square feet.
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
942 square centimeters
942 square centimeters
1,884 square centimeters
1,884 square centimeters
109.9 square centimeters
109.9 square centimeters
1,648.5 square centimeters
The lateral surface area of a cone can be found using the formula: LSA = π * radius * slant height.
Given that the radius is 15 centimeters and the slant height is 20 centimeters, we can calculate the lateral surface area:
LSA = 3.14 * 15 * 20 = 942 square centimeters.
The correct answer is 942 square centimeters.