Question
what is the surface area of a cone with a slant height of 22 cm and diameter of 25 cm? use 3.14 for pi.
Answers
Answer
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
Answer
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 of 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
Answered by
GPT 3.5
To find the surface area of a cone, we need to find the area of the base and the lateral surface area.
The diameter of the cone is 25 cm, so the radius (r) is half of that, which is 12.5 cm.
The formula for the lateral surface area of a cone is A = π * r * l, where l is the slant height.
Plugging in the values, we get:
A = 3.14 * 12.5 cm * 22 cm
A = 865 cm²
The formula for the base area of a cone is A = π * r².
Plugging in the values, we get:
A = 3.14 * (12.5 cm)²
A = 3.14 * 156.25 cm²
A = 490.625 cm²
To find the total surface area, we add the base area and the lateral surface area:
Total surface area = base area + lateral surface area
Total surface area = 490.625 cm² + 865 cm²
Total surface area = 1355.625 cm²
Therefore, the surface area of the cone is approximately 1355.625 cm².
The diameter of the cone is 25 cm, so the radius (r) is half of that, which is 12.5 cm.
The formula for the lateral surface area of a cone is A = π * r * l, where l is the slant height.
Plugging in the values, we get:
A = 3.14 * 12.5 cm * 22 cm
A = 865 cm²
The formula for the base area of a cone is A = π * r².
Plugging in the values, we get:
A = 3.14 * (12.5 cm)²
A = 3.14 * 156.25 cm²
A = 490.625 cm²
To find the total surface area, we add the base area and the lateral surface area:
Total surface area = base area + lateral surface area
Total surface area = 490.625 cm² + 865 cm²
Total surface area = 1355.625 cm²
Therefore, the surface area of the cone is approximately 1355.625 cm².
Answered by
GPT 3.5
To find the surface area of the spyglass, we need to calculate the area of the base and the lateral surface area.
The radius of the spyglass is 6 centimeters.
The formula for the lateral surface area of a cone is A = π * r * l, where l is the slant height.
Plugging in the values, we get:
A = 3.14 * 6 cm * 18 cm
A = 339.12 cm²
The formula for the base area of a cone is A = π * r².
Plugging in the values, we get:
A = 3.14 * (6 cm)²
A = 3.14 * 36 cm²
A = 113.04 cm²
To find the total surface area, we add the base area and the lateral surface area:
Total surface area = base area + lateral surface area
Total surface area = 113.04 cm² + 339.12 cm²
Total surface area = 452.16 cm²
Therefore, the surface area of the spyglass is approximately 452.16 cm².
The radius of the spyglass is 6 centimeters.
The formula for the lateral surface area of a cone is A = π * r * l, where l is the slant height.
Plugging in the values, we get:
A = 3.14 * 6 cm * 18 cm
A = 339.12 cm²
The formula for the base area of a cone is A = π * r².
Plugging in the values, we get:
A = 3.14 * (6 cm)²
A = 3.14 * 36 cm²
A = 113.04 cm²
To find the total surface area, we add the base area and the lateral surface area:
Total surface area = base area + lateral surface area
Total surface area = 113.04 cm² + 339.12 cm²
Total surface area = 452.16 cm²
Therefore, the surface area of the spyglass is approximately 452.16 cm².
Answered by
GPT 3.5
To find the surface area of the hourglass sculpture, we need to calculate the area of the two cones.
The diameter of each cone is 8 feet, so the radius (r) is half of that, which is 4 feet.
The formula for the lateral surface area of a cone is A = π * r * l, where l is the slant height.
Plugging in the values, we get:
A1 = 3.14 * 4 feet * 5 feet
A1 = 62.8 square feet
Since the hourglass sculpture consists of two identical cones, the total surface area for the outside of the sculpture is twice that amount:
Total surface area = 2 * A1
Total surface area = 2 * 62.8 square feet
Total surface area = 125.6 square feet
Therefore, approximately 125.6 square feet of steel is needed for the outside of the hourglass sculpture.
The diameter of each cone is 8 feet, so the radius (r) is half of that, which is 4 feet.
The formula for the lateral surface area of a cone is A = π * r * l, where l is the slant height.
Plugging in the values, we get:
A1 = 3.14 * 4 feet * 5 feet
A1 = 62.8 square feet
Since the hourglass sculpture consists of two identical cones, the total surface area for the outside of the sculpture is twice that amount:
Total surface area = 2 * A1
Total surface area = 2 * 62.8 square feet
Total surface area = 125.6 square feet
Therefore, approximately 125.6 square feet of steel is needed for the outside of the hourglass sculpture.
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