What is the total surface area of a right circular cone whose height is 14 cm and base radius is 7 cm?

Problem Restatement

Find the total surface area (TSA) of a right circular cone given its height and base radius.

Given data

• Height, h = 14 cm
• Radius, r = 7 cm
• Slant height, l = √(r^2 + h^2)

Concept / Formula

• Slant height: l = √(r^2 + h^2)
• Total surface area: TSA = πr(l + r)

Step-by-step calculation

l = √(7^2 + 14^2) = √(49 + 196) = √245 = 7√5 ≈ 15.652TSA = π × 7 × (15.652 + 7)Using π = 22/7 → TSA = (22/7) × 7 × 22.652 = 22 × 22.652 = 498.35 cm^2 (approx.)

Checks & Notes

• Using exact form: TSA = 49π(√5 + 1) cm^2.
• Always include both lateral area and base area when TSA is asked.

Final Answer

Total surface area ≈ 498.35 cm^2.