What is the surface area of the cone? Use 3.14 for pi.
Slant height= 22cm
Diameter= 25 cm
The correcct answer is 1,354.125
but how do u do it step by step
To find the surface area of a cone, you need to know the slant height and the diameter.
1) Start by finding the radius of the cone by dividing the diameter by 2:
radius = diameter / 2
radius = 25 cm / 2
radius = 12.5 cm
2) Next, calculate the height of the cone using the Pythagorean theorem:
height^2 = slant height^2 - radius^2
height^2 = 22 cm^2 - 12.5 cm^2
height^2 = 484 cm^2 - 155.25 cm^2
height^2 = 328.75 cm^2
height = √328.75 cm
height ≈ 18.13 cm
3) Calculate the lateral surface area of the cone:
lateral surface area = π * radius * slant height
lateral surface area = 3.14 * 12.5 cm * 22 cm
lateral surface area ≈ 867.5 cm^2
4) Finally, calculate the total surface area by adding the base area:
surface area = lateral surface area + π * radius^2
surface area = 867.5 cm^2 + 3.14 * 12.5 cm^2
surface area = 867.5 cm^2 + 39.25 cm^2
surface area ≈ 906.75 cm^2
The correct answer should be 906.75 cm^2, not 1,354.125 cm^2. Please double-check the correctness of the given answer.
Do this problem with the answer 1,354.125
Apologies for the confusion in my initial response. To calculate the surface area of the cone with the given answer of 1,354.125 cm^2, we can reverse-engineer the steps.
1) Start by finding the radius of the cone by dividing the diameter by 2:
radius = diameter / 2
radius = 25 cm / 2
radius = 12.5 cm
2) Next, calculate the height of the cone using the Pythagorean theorem:
height^2 = slant height^2 - radius^2
height^2 = 22 cm^2 - 12.5 cm^2
height^2 = 484 cm^2 - 155.25 cm^2
height^2 = 328.75 cm^2
height = √328.75 cm
height ≈ 18.13 cm
3) Calculate the lateral surface area of the cone:
lateral surface area = π * radius * slant height
lateral surface area = 3.14 * 12.5 cm * 22 cm
lateral surface area ≈ 867.5 cm^2
4) Finally, calculate the total surface area by adding the base area:
surface area = lateral surface area + π * radius^2
surface area = 867.5 cm^2 + 3.14 * 12.5 cm^2
surface area = 867.5 cm^2 + 39.25 cm^2
surface area ≈ 906.75 cm^2
As you can see, the calculated surface area is 906.75 cm^2, not 1,354.125 cm^2. Please ensure the accuracy of the given answer.