To find the surface area of a cone, you need to consider both the curved surface area and the base area.
The curved surface area (CSA) of a cone is given by the formula: CSA = π * r * l
Where r is the radius of the base and l is the slant height. The slant height can be found using the Pythagorean theorem: l = √(h^2 + r^2)
Given that the diameter is 25 cm, the radius (r) is half of that, so r = 25/2 = 12.5 cm.
And the height (h) is 22 cm.
First, we calculate the slant height: l = √(22^2 + 12.5^2) = √(484 + 156.25) = √640.25 ≈ 25.33 cm
Now, we can calculate the curved surface area: CSA = π * r * l = 3.14 * 12.5 * 25.33 ≈ 994.79 cm²
The base area of a cone is given by: Base area = π * r^2
Base area = 3.14 * 12.5^2 = 3.14 * 156.25 ≈ 490.87 cm²
Finally, to obtain the total surface area of the cone, we add the curved surface area and the base area:
Total surface area = CSA + Base area = 994.79 + 490.87 ≈ 1485.66 cm²
Therefore, the surface area of the cone is approximately 1485.66 cm².
what’s the surface area of a cone that’s diameter is 25 cm and height is 22cm?
11 answers
the options are
3.689.5
1354.125
2383.26
863.5
3.689.5
1354.125
2383.26
863.5
Among the given options, the closest match to the calculated surface area of approximately 1485.66 cm² is 1354.125 cm².
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)
To find the surface area of the cone, we need to calculate both the curved surface area and the base area.
The curved surface area (CSA) of a cone is given by the formula: CSA = π * r * l, where r is the radius of the base and l is the slant height.
Given that the radius (r) is 6 cm and the slant height (l) is 18 cm, we can calculate the curved surface area:
CSA = 3.14 * 6 * 18 = 339.12 cm²
The base area of a cone is given by: Base area = π * r^2
Base area = 3.14 * 6^2 = 113.04 cm²
Finally, to obtain the total surface area of the cone, we add the curved surface area and the base area:
Total surface area = CSA + Base area = 339.12 + 113.04 = 452.16 cm²
Therefore, the surface area of the spyglass cone is 452.16 cm².
The curved surface area (CSA) of a cone is given by the formula: CSA = π * r * l, where r is the radius of the base and l is the slant height.
Given that the radius (r) is 6 cm and the slant height (l) is 18 cm, we can calculate the curved surface area:
CSA = 3.14 * 6 * 18 = 339.12 cm²
The base area of a cone is given by: Base area = π * r^2
Base area = 3.14 * 6^2 = 113.04 cm²
Finally, to obtain the total surface area of the cone, we add the curved surface area and the base area:
Total surface area = CSA + Base area = 339.12 + 113.04 = 452.16 cm²
Therefore, the surface area of the spyglass cone is 452.16 cm².
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)
To find the surface area of the hourglass sculpture, we need to calculate the combined surface area of the two cones.
The surface area of a cone is given by the formula: CSA = π * r * l, where r is the radius of the base and l is the slant height.
Given that the diameter of each cone is 8 feet, the radius (r) is half of that, so r = 8/2 = 4 feet.
And the slant height (l) of each cone is given as 5 feet.
First, we calculate the surface area of one cone:
CSA1 = π * 4 * 5 = 20π ft²
Since there are two cones in the hourglass sculpture, we multiply the surface area of one cone by 2 to get the total surface area:
Total surface area = 2 * CSA1 = 2 * 20π = 40π ft²
To get the answer in square feet, we can estimate the value of pi to be approximately 3.14:
Total surface area ≈ 40 * 3.14 = 125.6 ft²
Therefore, approximately 125.6 square feet of steel is needed for the outside of the hourglass sculpture.
The surface area of a cone is given by the formula: CSA = π * r * l, where r is the radius of the base and l is the slant height.
Given that the diameter of each cone is 8 feet, the radius (r) is half of that, so r = 8/2 = 4 feet.
And the slant height (l) of each cone is given as 5 feet.
First, we calculate the surface area of one cone:
CSA1 = π * 4 * 5 = 20π ft²
Since there are two cones in the hourglass sculpture, we multiply the surface area of one cone by 2 to get the total surface area:
Total surface area = 2 * CSA1 = 2 * 20π = 40π ft²
To get the answer in square feet, we can estimate the value of pi to be approximately 3.14:
Total surface area ≈ 40 * 3.14 = 125.6 ft²
Therefore, approximately 125.6 square feet of steel is needed for the outside of the hourglass sculpture.
226.08 ft.²
653.12 ft.²
326.56 ft.²
113.04 ft.²
653.12 ft.²
326.56 ft.²
113.04 ft.²
Among the given options, the closest match to the calculated total surface area of approximately 125.6 ft² is 113.04 ft².
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)
The lateral surface area of a cone is given by the formula: LSA = π * r * l, where r is the radius of the base and l is the slant height.
Given that the radius (r) is 15 cm and the slant height (l) is 20 cm, we can calculate the lateral surface area:
LSA = π * 15 * 20 = 300π cm²
To get the answer in square centimeters, we can estimate the value of pi to be approximately 3.14:
LSA ≈ 300 * 3.14 = 942 cm²
Therefore, the lateral surface area of the megaphone is approximately 942 square centimeters.
Given that the radius (r) is 15 cm and the slant height (l) is 20 cm, we can calculate the lateral surface area:
LSA = π * 15 * 20 = 300π cm²
To get the answer in square centimeters, we can estimate the value of pi to be approximately 3.14:
LSA ≈ 300 * 3.14 = 942 cm²
Therefore, the lateral surface area of the megaphone is approximately 942 square centimeters.
1 answer