What is the surface area in square centimeters, of a cone with a diameter of 13 feet and a slant of 14 feet? used 3.13 for pi and round to the nearest tenth, if necessary
To find the surface area of a cone, we need to know the radius and height.
Given that the diameter of the cone is 13 feet, the radius would be half of that, which is 13/2 = 6.5 feet.
To find the height, we can use the Pythagorean theorem. The slant height (s) is given as 14 feet, and the radius (r) is given as 6.5 feet.
Using the Pythagorean theorem, we have: s² = r² + h²
14² = 6.5² + h²
196 = 42.25 + h²
h² = 196 - 42.25
h² = 153.75
h ≈ √153.75
h ≈ 12.4 feet
Now that we have the radius and height, we can calculate the surface area of the cone.
The curved surface area of a cone can be found using the formula A = πrs, where r is the radius and s is the slant height.
A = 3.13 × 6.5 × 14
A ≈ 282.27 square feet
To convert this to square centimeters, we multiply by the conversion factor 929.03 (1 square foot = 929.03 square centimeters):
A ≈ 282.27 × 929.03
A ≈ 262,252.29 square centimeters
Therefore, the surface area of the cone is approximately 262,252.29 square centimeters, rounded to the nearest tenth.