Surface Area of Cones Practice

Question

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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.

Answer 1

To calculate the surface area of a cone, we need to know both the area of the base (a circle) and the lateral surface area (the area of the cone's side). The total surface area (SA) is the sum of the base area and lateral surface area.

First, let's calculate the area of the base of the cone, which is a circle.

\[ \text{Base Area} = \pi r^2 \]
where \(\pi \approx 3.14\) and \(r\) is the radius of the base.

Plugging in the given values:
\[ \text{Base Area} = 3.14 \times 6^2 \]
\[ \text{Base Area} = 3.14 \times 36 \]
\[ \text{Base Area} = 113.04 \]

Next, let's calculate the lateral surface area of the cone, a.k.a. the cone's side.

The lateral surface area (LSA) is given by the formula:
\[ \text{LSA} = \pi r l \]
where \(l\) is the slant height (side) of the cone.

Based on the information provided:
\[ \text{LSA} = 3.14 \times 6 \times 11 \]
\[ \text{LSA} = 3.14 \times 66 \]
\[ \text{LSA} = 207.24 \]

Now, let's find the total surface area:
\[ \text{SA} = \text{Base Area} + \text{LSA} \]
\[ \text{SA} = 113.04 + 207.24 \]
\[ \text{SA} = 320.28 \]

Thus, the surface area of the cone, rounded to the nearest tenth, is:
\[ \text{SA} \approx 320.3 \] square units.

Answer 2

the answer to the question is 320.3 for anyone who is still doing this

Answer 3

wrong