Given:
- Area of the base of a right circular cone = 78.5 sq.cm
- Height of the cone = 12 cm

To find:
- Volume of the cone
- Curved surface area of the cone

Solution:
Step 1: Finding the radius of the cone
- The area of the base of a cone is given by the formula:
Area = π * r^2, where r is the radius of the base
- Given area of the base = 78.5 sq.cm
- Substituting the values in the formula, we get:
78.5 = π * r^2
- Dividing both sides of the equation by π, we get:
r^2 = 78.5 / π
- Taking square root on both sides, we get:
r = √(78.5 / π)

Step 2: Finding the volume of the cone
- The volume of a cone is given by the formula:
Volume = (1/3) * π * r^2 * h, where h is the height of the cone
- Given height of the cone = 12 cm
- Substituting the values in the formula, we get:
Volume = (1/3) * π * (√(78.5 / π))^2 * 12
- Simplifying the equation, we get:
Volume = (1/3) * π * (78.5 / π) * 12

Step 3: Finding the curved surface area of the cone
- The curved surface area of a cone is given by the formula:
CSA = π * r * l, where l is the slant height of the cone
- The slant height of the cone can be found using the Pythagorean theorem:
l^2 = r^2 + h^2
- Substituting the values, we get:
l^2 = (√(78.5 / π))^2 + 12^2
- Simplifying the equation, we get:
l^2 = 78.5 / π + 144
- Taking square root on both sides, we get:
l = √(78.5 / π + 144)
- Substituting the values in the formula for CSA, we get:
CSA = π * (√(78.5 / π)) * √(78.5 / π + 144)

Step 4: Calculating the values
- Using the given value of π as 3.14, we can substitute the values in the formulas to calculate the volume and curved surface area of the cone.

Final Answer:
- The volume of the cone is (1/3) * π * (78.5 / π) * 12 cubic cm.
- The curved surface area of the cone is π * (√(78.5 / π)) * √(78.5 / π + 144) sq.cm.