A cone shows a radius of 6 and hypotenuse or side as 11.
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
To find the surface area of a cone, we need to find the slant height of the cone first.
We can use the Pythagorean theorem to find the slant height.
The radius (r) is given as 6, and the hypotenuse (h) is given as 11.
Using the Pythagorean theorem, we have:
r^2 + slant height^2 = h^2
Plugging in the values:
6^2 + slant height^2 = 11^2
36 + slant height^2 = 121
slant height^2 = 121 - 36
slant height^2 = 85
Taking the square root of both sides, we get:
slant height = sqrt(85)
slant height ≈ 9.2
Now that we have the slant height, we can calculate the surface area of the cone.
The formula to find the surface area of a cone is:
Surface area = πr^2 + πrl
Given that the radius (r) is 6 and the slant height (l) is approximately 9.2, and using 3.14 for pi, we have:
Surface area = 3.14 * 6^2 + 3.14 * 6 * 9.2
Surface area = 3.14 * 36 + 3.14 * 55.2
Surface area = 113.04 + 173.328
Surface area ≈ 286.37
Therefore, the surface area of the cone is approximately 286.4 square units.