To find the surface area of the cone, we need to calculate two areas: the base area and the lateral (side) surface area. The total surface area of the cone is the sum of these two areas.
First, we find the radius of the cone. Since the diameter is 6 inches, we divide it by 2 to get the radius:
Radius = Diameter / 2
Radius = 6 in / 2
Radius = 3 in
Now, we need to calculate the slant height of the cone. The slant height (l), the height of the cone (h), and the radius of the base (r) form a right triangle. We can use the Pythagorean theorem to find the slant height:
l^2 = r^2 + h^2
l^2 = 3^2 + 4^2
l^2 = 9 + 16
l^2 = 25
l = √25
l = 5 in
Next, we calculate the lateral surface area (LSA), which is the area of the cone's side. The formula for the lateral surface area of a cone is:
LSA = π * r * l
LSA = π * 3 in * 5 in
Using the numeric result from the Python code:
LSA ≈ 47.12 in^2
Then, we find the base area (BA), which is simply the area of the circular base of the cone. The formula for the area of a circle is:
BA = π * r^2
BA = π * (3 in)^2
Again using the numeric result from the Python code:
BA ≈ 28.27 in^2
Finally, we sum the lateral surface area and the base area to find the total surface area (SA) of the cone:
SA = LSA + BA
SA ≈ 47.12 in^2 + 28.27 in^2
SA ≈ 75.39 in^2
Looking at the given multiple-choice options, we round the number to one decimal place as follows:
SA ≈ 75.4 in^2
So the correct answer is:
B 75.4 in^2
