A circular cone has a diameter of 8 in. and a slant height of 10 in. What is the surface area of the cone to the nearest inch?(1 point)
Responses
452 in.2
452 in. squared
176 in.2
176 in. squared
302 in.2
302 in. squared
63 in.2
To find the surface area of a cone, we need to find the area of the base and the lateral surface area.
The diameter of the cone is 8 in, so the radius is half of that, which is 4 in. The formula for the area of a circle is A = πr^2, so the area of the base is π(4^2) = 16π.
The slant height of the cone is 10 in. The lateral surface area of a cone can be found using the formula LSA = πrl, where r is the radius and l is the slant height. So the lateral surface area is π(4)(10) = 40π.
To find the total surface area, we add the area of the base and the lateral surface area: 16π + 40π = 56π.
To find the surface area to the nearest inch, we need to approximate the value of π. π is approximately 3.14.
Therefore, the surface area of the cone is approximately 56π = 56(3.14) ≈ 176 in.2.
Hence, the surface area of the cone is 176 in.2.