What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
(1 point)
Sorry, you need to provide the dimensions of the cone (radius and height) in order to calculate its surface area.
The slant is 11 and the radius is 6
wrong
still wrong
To calculate the surface area of a cone, you need to consider the curved surface area (lateral area) and the base area.
The curved surface area of a cone can be calculated using the formula: π * radius * slant height
Given:
Radius (r) = 6
Slant height (l) = 11
Curved Surface Area = π * 6 * 11
Using π ≈ 3.14, we can calculate the surface area as follows:
Curved Surface Area = 3.14 * 6 * 11
= 207.48
To round it to the nearest tenth, the surface area of the cone is approximately 207.5 square units.
Apologies for the mistake. Let's calculate the correct surface area of the cone.
To calculate the surface area of a cone, you need to consider the curved surface area (lateral area) and the base area.
The curved surface area of a cone can be calculated using the formula: π * radius * slant height, where the slant height can be calculated using the Pythagorean theorem: slant height = √(radius^2 + height^2)
Given:
Radius (r) = 6
Slant height (l) = 11
Slant height (l) = √(radius^2 + height^2)
11 = √(6^2 + height^2)
11^2 = 6^2 + height^2
121 = 36 + height^2
height^2 = 121 - 36
height^2 = 85
height = √85
Now that we have the slant height and the radius, we can calculate the curved surface area:
Curved Surface Area = π * radius * slant height
= 3.14 * 6 * 11
= 207.48
To round it to the nearest tenth, the surface area of the cone is approximately 207.5 square units.
Apologies once again for the mistake. Let's recalculate the surface area of the cone using the correct formula.
The surface area of a cone includes the curved surface area (lateral area) and the base area.
Given:
Radius (r) = 6
Slant height (l) = 11
To find the curved surface area, we'll first find the height of the cone using the Pythagorean theorem:
height^2 = slant height^2 - radius^2
height^2 = 11^2 - 6^2
height^2 = 121 - 36
height^2 = 85
height = √85
Now we can calculate the surface area:
Curved surface area = π * radius * slant height
= 3.14 * 6 * 11
= 205.92 (rounded to the nearest tenth)
The base area of a cone is given by the formula:
Base area = π * radius^2
= 3.14 * 6^2
= 113.04 (rounded to the nearest tenth)
To find the total surface area, we add the curved surface area and the base area:
Total surface area = Curved surface area + Base area
= 205.92 + 113.04
= 318.96 (rounded to the nearest tenth)
Therefore, the surface area of the cone is approximately 319 square units.