Final answer:
The curved surface area of the cone is 220 cm² and the total surface area is 374 cm², calculated using the formulas for a circular cone's surface areas.
Step-by-step explanation:
The question asks to find the curved surface area and total surface area of a right circular cone with slant height of 10 cm and base radius of 7 cm.
To find the curved surface area (CSA), we use the formula:
CSA = πrℓ where r is the radius and ℓ is the slant height. For this cone, CSA = π * 7 cm * 10 cm = 220 cm² (since π is approximately 3.14).
The base area of the cone is calculated using the formula for the area of a circle: A = πr². Therefore, the base area of the cone is π * 7² cm² = 154 cm².
The total surface area (TSA) of the cone is the sum of the base area and the curved surface area: TSA = CSA + base area = 220 cm² + 154 cm² = 374 cm².