Question
The cone has a diameter of 14 inches and a slant height of 20 inches. Find the surface area to the nearest hundredth. Need units. show work.
Answers
GPT 3.5
First, we need to find the radius of the cone. The diameter is given as 14 inches, so the radius is half of that, which is 7 inches.
Next, we can use the slant height to find the height of the cone. We can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (in this case, the height and the radius).
Let h be the height of the cone. Then we have:
h^2 + 7^2 = 20^2
h^2 + 49 = 400
h^2 = 351
h = √351 ≈ 18.7 (rounded to the nearest tenth)
Now we can calculate the surface area of the cone. The formula for the surface area of a cone is:
Surface Area = πr^2 + πrl
where r is the radius and l is the slant height. Plugging in the values we found, we have:
Surface Area = π(7^2) + π(7)(20)
Surface Area ≈ 153.94
Therefore, the surface area of the cone is approximately 153.94 square inches (rounded to the nearest hundredth).
Next, we can use the slant height to find the height of the cone. We can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (in this case, the height and the radius).
Let h be the height of the cone. Then we have:
h^2 + 7^2 = 20^2
h^2 + 49 = 400
h^2 = 351
h = √351 ≈ 18.7 (rounded to the nearest tenth)
Now we can calculate the surface area of the cone. The formula for the surface area of a cone is:
Surface Area = πr^2 + πrl
where r is the radius and l is the slant height. Plugging in the values we found, we have:
Surface Area = π(7^2) + π(7)(20)
Surface Area ≈ 153.94
Therefore, the surface area of the cone is approximately 153.94 square inches (rounded to the nearest hundredth).