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
2,383.26 square centimeters
2,383.26 square centimeters
863.5 square centimeters
To find the surface area of the cone, we need to calculate the lateral surface area and the base area, then add them together.
The lateral surface area of a cone can be found using the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height of the cone.
Given that the base diameter is 25 centimeters, the radius is half of that: r = 25/2 = 12.5 cm.
The slant height (hypotenuse) is given as 22 centimeters.
Using the Pythagorean theorem, we can find the height of the cone (h) by solving for h in the equation: h^2 = ℓ^2 - r^2.
h^2 = 22^2 - 12.5^2
h^2 = 484 - 156.25
h^2 = 327.75
h ≈ √327.75
h ≈ 18.1 cm (rounded to one decimal place)
Now, we can calculate the lateral surface area:
L = πrℓ
L = 3.14 * 12.5 * 22
L ≈ 3.14 * 275
L ≈ 863.5 square centimeters
The area of the base of the cone is given by the formula: B = πr^2.
B = 3.14 * (12.5^2)
B = 3.14 * 156.25
B ≈ 490.625 square centimeters
Finally, we can find the surface area by adding the lateral surface area (L) and the base area (B):
Surface Area = L + B
Surface Area ≈ 863.5 + 490.625
Surface Area ≈ 1354.125 square centimeters.
Therefore, the correct answer is 1,354.125 square centimeters.