Question

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.

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

The surface area of a cone consists of two parts: the base area and the lateral surface area. Since we have the radius (r = 6) and the slant height (l = side = 11), we can use these to calculate the surface area.

Base Area (A_base) = π * r^2
Lateral Surface Area (A_lateral) = π * r * l

Let's calculate the base area first:
A_base = π * r^2
A_base = 3.14 * 6^2
A_base = 3.14 * 36
A_base = 113.04 square units

Now, let's calculate the lateral surface area:
A_lateral = π * r * l
A_lateral = 3.14 * 6 * 11
A_lateral = 3.14 * 66
A_lateral = 207.24 square units

To find the total surface area, we sum the base area and the lateral surface area:
Total Surface Area = A_base + A_lateral
Total Surface Area = 113.04 + 207.24
Total Surface Area = 320.28 square units

Rounding to the nearest tenth, the surface area of the cone is approximately 320.3 square units.