An open (hollow) right circular cone of height 12 cm and base diameter 14 cm is to be made from an iron sheet. Find the area of sheet required (take the curved surface area only).

Introduction / Context:Sheet-metal problems for cones typically require the curved surface area (CSA) of a right circular cone, since the base is usually open for containers or funnels. We compute CSA using radius and slant height.

Given Data / Assumptions:

• Height h = 12 cm.
• Base diameter = 14 cm ⇒ radius r = 7 cm.
• Only curved surface area is needed (open cone).
• Use π = 22/7 for exact cancellation with r = 7 cm.

Concept / Approach:

• Slant height l = sqrt(r^2 + h^2).
• Curved surface area: CSA = π*r*l.

Step-by-Step Solution:

Verification / Alternative check:Using π ≈ 3.14 and l ≈ 13.89: CSA ≈ 3.14*7*13.89 ≈ 305.8 cm^2. Rounding to the nearest provided option gives 304 sq cm, consistent with standard exam rounding.

Why Other Options Are Wrong:

• 504/704/804 sq cm: Significantly larger than precise CSA; these might reflect including a base or using wrong slant height.
• None of these: Incorrect because 304 sq cm matches the computed value by rounding.

Common Pitfalls:

• Confusing height with slant height.
• Including base area when asked for a hollow cone.
• Rounding too early; compute l first then CSA.

Final Answer:304 sq cm