I need to find the approximate surface area of a cone with the R=5 and L=6. I thought I figured it out by 3.14(5)(6) which will give me 94.2 I then would take 94.2 +3.14(5)squared and I came up with 172.7, but my answer should be either 20m squared, 98m squared, 118m squared or 67m squared, what did I do wrong?

I think you have written it down wrong. If the diameter of the cone is 5, then R=2.5 and the area is 66.7, or 67.

To find the surface area of a cone, you need to consider two parts: the base and the lateral surface.

First, let's calculate the base area. The base of a cone is a circle, and the formula for the area of a circle is A = πr^2, where r is the radius. In this case, the radius (R) is given as 5. So, the base area is A_base = π(5)^2.

Next, let's calculate the lateral surface area. The formula for the lateral surface area of a cone is A_lateral = πrL, where L is the slant height. In this case, the slant height (L) is given as 6.

Now, you correctly calculated the lateral surface area: A_lateral = π(5)(6) = 30π.

To calculate the total surface area, you need to add the base area and the lateral surface area. So, the total surface area (A_total) is A_base + A_lateral.

Using the values we calculated, A_total = π(5^2) + 30π = 25π + 30π = 55π.

Now, we can approximate this value. Assuming π ≈ 3.14, we can evaluate: 55 × 3.14 ≈ 172.7.

So, your calculation for the total surface area appears to be correct. However, the given answer choices are in square meters (m^2), but you did not mention any units in your question. If the units are in meters, then the answer should be approximately 172.7m^2. It appears that there is no exact match among the given answer choices of 20m^2, 98m^2, 118m^2, or 67m^2.