Use the image to answer the question.
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.
(1 point)
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It seems that the image is missing, so I am unable to provide the surface area of the cone based on the given information.
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.
It says it wrong... you know what its ok Ill just go to brainly
To find the surface area of a cone, we need to calculate the lateral surface area and the base area separately and then add them together.
The lateral surface area of a cone can be found using the formula: $$ LSA = \pi \times r \times l$$
where r is the radius of the cone and l is the slant height.
To find the slant height, we can use the Pythagorean theorem. The hypotenuse of the right triangle formed by the radius and the slant height is equal to the side of the cone, which is given as 11. So, using the Pythagorean theorem, we can find the slant height, l:
$$ l^2 = 11^2 - 6^2 $$
$$ l^2 = 121 - 36 $$
$$ l^2 = 85 $$
$$ l = \sqrt{85} $$
Now we can calculate the lateral surface area:
$$ LSA = 3.14 \times 6 \times \sqrt{85} $$
Rounding to the nearest tenth:
$$ LSA \approx 3.14 \times 6 \times 9.2 \approx 170.13 $$
The area of the base of the cone is given by the formula:
$$ Base \, Area = \pi \times r^2 $$
$$ Base \, Area = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 $$
Now we can find the total surface area by adding the lateral surface area and the base area:
$$ Total \, Surface \, Area = LSA + Base \, Area = 170.13 + 113.04 = 283.17 $$
Therefore, the surface area of the cone is approximately 283.2 square units.
To find the surface area of a cone, we need to use the formula
Surface Area = π * r * (r + s)
where r is the radius of the base of the cone and s is the slant height.
In the given image, we are given the radius of the cone as 6 and the hypotenuse or slant height as 11. To find the slant height, we can use the Pythagorean theorem. In a right triangle formed by the height (h), radius (r), and the slant height (s), we have h^2 + r^2 = s^2.
Substituting the given values into the equation, we can solve for h:
h^2 + 6^2 = 11^2
h^2 + 36 = 121
h^2 = 121 - 36
h^2 = 85
h = √85
Now that we have the slant height (s) and the radius (r), we can substitute these values into the surface area formula:
Surface Area = π * 6 * (6 + √85)
Using 3.14 as the value of π, we can calculate the surface area by multiplying:
Surface Area = 3.14 * 6 * (6 + √85)
Surface Area ≈ 3.14 * 6 * (6 + √85)
Surface Area ≈ 3.14 * 6 * (6 + 9.22)
Surface Area ≈ 3.14 * 6 * 15.22
Surface Area ≈ 287.934
Rounded to the nearest tenth, the surface area of the cone is approximately 287.9 square units.