To find the surface area of a cone, we need to find the area of the base and the lateral surface area.
The base of the cone is a circle with a diameter of 25 centimeters. The radius, which is half the diameter, is 25/2 = 12.5 centimeters. The area of the base can be calculated using the formula for the area of a circle: A = πr^2.
A = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 square centimeters
The lateral surface area can be calculated using the formula A = πr * l, where r is the radius and l is the slant height. The slant height can be found using the Pythagorean theorem since we know the height and the hypotenuse.
l^2 = h^2 + r^2
l^2 = 22^2 + 12.5^2
l^2 = 484 + 156.25
l^2 = 640.25
l ≈ 25.310 centimeters
Now we can calculate the lateral surface area:
A = 3.14 * 12.5 * 25.310 = 995.61 square centimeters
Finally, we add the area of the base and the lateral surface area to find the total surface area of the cone:
Total surface area = base area + lateral surface area
Total surface area = 490.625 + 995.61 = 1,486.235 square centimeters
Rounded to the nearest tenth, the surface area of the cone is approximately 1,486.2 square centimeters.
Therefore, the correct answer is:
1,486.2 square centimeters
Surface Area of Cones Quick Check
2 of 52 of 5 Items
Question
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
3,689.5 square centimeters
3,689.5 square centimeters
1,354.125 square centimeters
1,354.125 square centimeters
863.5 square centimeters
863.5 square centimeters
2,383.26 square centimeters
5 answers
What is the surface area of the cone? Use 3.14 for pi.
(1 point)
Responses
3,689.5 square centimeters
3,689.5 square centimeters
1,354.125 square centimeters
1,354.125 square centimeters
863.5 square centimeters
863.5 square centimeters
2,383.26 square centimeters
(1 point)
Responses
3,689.5 square centimeters
3,689.5 square centimeters
1,354.125 square centimeters
1,354.125 square centimeters
863.5 square centimeters
863.5 square centimeters
2,383.26 square centimeters
The correct answer is not provided in the given options.
The surface area of the cone can be calculated by adding the area of the base and the lateral surface area.
1. Area of base:
The base is a circle with a diameter of 25 centimeters, so the radius is 25/2 = 12.5 centimeters. The area of the base is given by A = πr^2.
A = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 square centimeters
2. Lateral surface area:
The slant height, l, can be found using the Pythagorean theorem with the height, h, and the hypotenuse:
l^2 = h^2 + r^2
l^2 = 22^2 + (12.5)^2
l^2 = 484 + 156.25
l^2 = 640.25
l ≈ 25.310 centimeters
The lateral surface area is calculated using A = πr * l:
A = 3.14 * 12.5 * 25.310 = 995.6115 square centimeters (rounded to four decimal places)
Now, we can find the total surface area by adding the base area and the lateral surface area:
Total surface area = base area + lateral surface area = 490.625 + 995.6115 = 1,486.2365 square centimeters (rounded to four decimal places)
Therefore, the surface area of the cone is approximately 1,486.2 square centimeters.
The surface area of the cone can be calculated by adding the area of the base and the lateral surface area.
1. Area of base:
The base is a circle with a diameter of 25 centimeters, so the radius is 25/2 = 12.5 centimeters. The area of the base is given by A = πr^2.
A = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 square centimeters
2. Lateral surface area:
The slant height, l, can be found using the Pythagorean theorem with the height, h, and the hypotenuse:
l^2 = h^2 + r^2
l^2 = 22^2 + (12.5)^2
l^2 = 484 + 156.25
l^2 = 640.25
l ≈ 25.310 centimeters
The lateral surface area is calculated using A = πr * l:
A = 3.14 * 12.5 * 25.310 = 995.6115 square centimeters (rounded to four decimal places)
Now, we can find the total surface area by adding the base area and the lateral surface area:
Total surface area = base area + lateral surface area = 490.625 + 995.6115 = 1,486.2365 square centimeters (rounded to four decimal places)
Therefore, the surface area of the cone is approximately 1,486.2 square centimeters.
not this answer give me answerrrrrrr
I apologize for the confusion. The correct answer is not provided in the given options.
To find the surface area of a cone, we need to calculate the area of the base and the lateral surface area.
1. Area of the base:
The base of the cone is a circle with a diameter of 25 centimeters. The radius is half of the diameter, so the radius is 25/2 = 12.5 centimeters. The area of the base can be found using the formula A = πr^2.
A = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 square centimeters
2. Lateral surface area:
The slant height, l, can be found using the Pythagorean theorem. The height, h, and the hypotenuse, which is the side of the cone, are given.
l^2 = h^2 + r^2
l^2 = 22^2 + (12.5)^2
l^2 = 484 + 156.25
l^2 = 640.25
l ≈ 25.310 centimeters
The lateral surface area can be calculated using A = πr * l:
A = 3.14 * 12.5 * 25.310 = 995.6125 square centimeters (rounded to four decimal places)
Finally, we can find the total surface area by adding the base area and the lateral surface area:
Total surface area = base area + lateral surface area = 490.625 + 995.6125 = 1486.2375 square centimeters (rounded to four decimal places)
Therefore, the correct answer is approximately 1486.2 square centimeters.
To find the surface area of a cone, we need to calculate the area of the base and the lateral surface area.
1. Area of the base:
The base of the cone is a circle with a diameter of 25 centimeters. The radius is half of the diameter, so the radius is 25/2 = 12.5 centimeters. The area of the base can be found using the formula A = πr^2.
A = 3.14 * (12.5)^2 = 3.14 * 156.25 = 490.625 square centimeters
2. Lateral surface area:
The slant height, l, can be found using the Pythagorean theorem. The height, h, and the hypotenuse, which is the side of the cone, are given.
l^2 = h^2 + r^2
l^2 = 22^2 + (12.5)^2
l^2 = 484 + 156.25
l^2 = 640.25
l ≈ 25.310 centimeters
The lateral surface area can be calculated using A = πr * l:
A = 3.14 * 12.5 * 25.310 = 995.6125 square centimeters (rounded to four decimal places)
Finally, we can find the total surface area by adding the base area and the lateral surface area:
Total surface area = base area + lateral surface area = 490.625 + 995.6125 = 1486.2375 square centimeters (rounded to four decimal places)
Therefore, the correct answer is approximately 1486.2 square centimeters.