Answer: The formula for the surface area of a cone is S = π * r * s + π * r², where r is the radius of the base and s is the slant height of the cone.
To find the surface area of a cone, you first need to find the radius of the base. Since the base diameter is given as 7cm, you can divide this by 2 to find the radius of the base:
r = 7cm / 2 = 3.5cm
Next, you need to find the slant height of the cone. You can use the Pythagorean theorem to do this.
slant height = sqrt(r^2 + h^2) = sqrt(3.5² + 8²) = sqrt(12.25 + 64) = sqrt(76.25) = 8.766cm
Now you can substitute these values into the formula for the surface area of a cone and find the surface area of the cone.
S = π * r * s + π * r² = π * 3.5cm * 8.766cm + π * 3.5² cm² = 12.571 cm² + 38.485 cm² = 51.056 cm²
So the surface area of a cone with a base diameter of 7cm and height of 8cm is 51.056 cm²
Explanation: