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)
$$
Skip to navigation
5 answers
It seems that the image is missing, so I am unable to provide the surface area of the cone based on the given information.
A cone shows a radius of 6 and hypotenuse or side as 11.
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
To find the surface area of a cone, we need to calculate the lateral surface area and the base area separately and then add them together.
The lateral surface area of a cone can be found using the formula: $$ 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 $$
Therefore, the surface area of the cone is approximately 283.2 square units.
The lateral surface area of a cone can be found using the formula: $$ 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.
It says it wrong... you know what its ok Ill just go to brainly
Apologies for any confusion caused. If you need further assistance, feel free to ask.