What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
Radious = 6
Length = 11
To find the surface area of the cone, we need to calculate the lateral surface area and the base area separately.
The lateral surface area of a cone is given by L = πrℓ, where r is the radius and ℓ is the slant height (the length from the apex to a point on the circumference of the base).
Given:
Radius (r) = 6
Length (ℓ) = 11
We can calculate the slant height using the Pythagorean theorem:
ℓ = √(r^2 + h^2), where h is the height of the cone. However, the height is not given, so we cannot calculate the exact slant height. We need additional information to find the height.
Assuming the cone is a right cone (the axis is perpendicular to the base), we can use the Pythagorean theorem with the height (h) and the radius (r) to find the slant height:
ℓ = √(r^2 + h^2)
11 = √(6^2 + h^2)
11 = √(36 + h^2)
121 = 36 + h^2
h^2 = 121 - 36
h^2 = 85
h = √85 ≈ 9.22 (rounded to the nearest hundredth)
With the slant height, we can calculate the lateral surface area:
L = πrℓ
L = 3.14 × 6 × 9.22
L ≈ 172.51 (rounded to the nearest hundredth)
Next, we need to find the base area of the cone.
The base area of a cone is given by A = πr^2, where r is the radius.
Given:
Radius (r) = 6
We can calculate the base area:
A = πr^2
A = 3.14 × 6^2
A = 3.14 × 36
A ≈ 113.04 (rounded to the nearest hundredth)
Finally, we can find the total surface area by adding the lateral surface area and the base area:
Total Surface Area = L + A
Total Surface Area ≈ 172.51 + 113.04
Total Surface Area ≈ 285.55 (rounded to the nearest hundredth)
Therefore, the surface area of the cone is approximately 285.5 square units.