To calculate the total surface area of a solid cone, you need to consider the curved surface area and the base area.
Given:
Slant height (l) = 10 cm
Base diameter (d) = 10 cm
To calculate the curved surface area (CSA) of the cone, we can use the formula:
CSA = π * r * l
where r is the radius of the base of the cone. Since the base diameter is given as 10 cm, the radius (r) is half of the diameter:
r = d/2 = 10 cm / 2 = 5 cm
Now, let's calculate the curved surface area:
CSA = π * r * l
= 3.14 * 5 cm * 10 cm
= 157 cm²
Next, to calculate the base area (BA) of the cone, we use the formula:
BA = π * r²
BA = 3.14 * (5 cm)²
= 3.14 * 25 cm²
= 78.5 cm²
Finally, to find the total surface area (TSA) of the cone, we sum up the curved surface area and the base area:
TSA = CSA + BA
= 157 cm² + 78.5 cm²
= 235.5 cm²
Therefore, the total surface area of the solid cone is 235.5 cm².