Surface Area of Cones Practice
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Question
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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)
That wrong
someone just put the right answer already
To find the surface area of a cone, we need to calculate the lateral surface area and add it to the base area.
First, let's find the slant height of the cone using the Pythagorean Theorem. The radius is given as 6 and the hypotenuse or side is given as 11.
Using the Pythagorean Theorem, we can calculate the slant height (l):
l^2 = r^2 + h^2
l^2 = 6^2 + h^2
121 = 36 + h^2
h^2 = 121 - 36
h^2 = 85
h ≈ √85
h ≈ 9.22 (rounded to two decimal places)
Next, let's find the lateral surface area of the cone. The formula for the lateral surface area of a cone is:
Lateral surface area = π × r × l
Plugging in the values, we get:
Lateral surface area = 3.14 × 6 × 9.22
Lateral surface area ≈ 173.16 (rounded to two decimal places)
Lastly, let's find the base area of the cone. The formula for the base area of a cone is:
Base area = π × r^2
Plugging in the values, we get:
Base area = 3.14 × 6^2
Base area ≈ 113.04 (rounded to two decimal places)
Now, let's find the surface area by adding the lateral surface area and the base area:
Surface area = Lateral surface area + Base area
Surface area ≈ 173.16 + 113.04
Surface area ≈ 286.2 (rounded to one decimal place)
Therefore, the surface area of the cone is approximately 286.2 square units.
I apologize for the mistake. Let's correct the calculation for the surface area of the cone.
The formula for the surface area of a cone is given by:
Surface area = π × r × (r + l)
Where r is the radius of the cone and l is the slant height.
Given the radius as 6 and the slant height as 9.22 (rounded to two decimal places), we can plug in these values to calculate the surface area:
Surface area = 3.14 × 6 × (6 + 9.22)
Surface area ≈ 3.14 × 6 × 15.22
Surface area ≈ 287.12 (rounded to two decimal places)
Therefore, the surface area of the cone is approximately 287.12 square units.
To find the surface area of a cone, we need to use the formula:
Surface Area = π * r * (r + l)
Where:
- π is a constant equal to approximately 3.14
- r is the radius of the cone
- l is the slant height of the cone
In this case, the radius is given as 6 and the hypotenuse or side is given as 11. The hypotenuse is the same as the slant height.
So, we can substitute these values into the formula:
Surface Area = 3.14 * 6 * (6 + 11)
Now, we can evaluate this expression to find the surface area.
Surface Area = 3.14 * 6 * 17
Surface Area = 317.52
Rounded to the nearest tenth, the surface area of the cone is approximately 317.5.