The height of a right circular cone is 24 cm and the area of its circular base is 154 cm2. What is the curved surface area of the cone in square centimetres? Take pi = 22/7.

Introduction / Context:
This question involves a right circular cone and asks for its curved surface area, also known as the lateral surface area. The cone is described by the area of its base and its vertical height. To reach the curved surface area, one must first find the radius from the base area, then compute the slant height using the Pythagoras theorem, and finally apply the curved surface area formula. This chain of calculations is very typical in aptitude questions on mensuration.

Given Data / Assumptions:

• Base area of the cone = 154 cm2.
• Height of the cone h = 24 cm.
• The cone is right, so height is perpendicular to the base.
• Use pi = 22/7 where needed.
• We need the curved surface area in cm2.

Concept / Approach:
The base area of a cone is a circle with area pi * r^2. Once r is found from this equation, the slant height l can be obtained from l^2 = r^2 + h^2, because the radius, height, and slant height form a right triangle. The curved surface area of a right circular cone is given by pi * r * l. Each step relies on basic formulas that come from circle geometry and the Pythagoras theorem.

Step-by-Step Solution:
Step 1: Let r be the radius of the base. Base area = pi * r^2 = 154.Step 2: Using pi = 22/7, write (22/7) * r^2 = 154. Multiply both sides by 7 to get 22 * r^2 = 1078.Step 3: Solve for r^2 as r^2 = 1078 / 22 = 49, so r = 7 cm.Step 4: Height h = 24 cm. Use Pythagoras theorem to find slant height l: l^2 = r^2 + h^2 = 7^2 + 24^2 = 49 + 576 = 625, so l = 25 cm.Step 5: Curved surface area of the cone = pi * r * l = (22/7) * 7 * 25 = 22 * 25 = 550 cm2.

Verification / Alternative check:
The numbers are very convenient: r = 7, h = 24, and l = 25 form a Pythagorean triple with 7, 24, 25, which makes the computation clean. Also, base area for r = 7 and pi = 22/7 equals (22/7) * 49 = 154 cm2, which matches the given data. Curved surface area 550 cm2 is consistent with these values and no other combination of r and h would satisfy all these conditions simultaneously.

Why Other Options Are Wrong:

• 484 cm2 would correspond to a slant height smaller than 25 cm and does not match the base area relation.
• 525 cm2 suggests an incorrect multiplication, for example using 21 instead of 25 in the final step.
• 515 cm2 is a random value that does not arise from any standard combination of r, h, and l for the given data.
• 500 cm2 again is simply not supported by the exact calculations, which give 550 cm2 exactly.

Common Pitfalls:

• Using height instead of slant height in the curved surface area formula.
• Forgetting to use the correct value of pi or miscomputing the radius from the base area.
• Rounding intermediate values unnecessarily, which is not required here because the numbers work out nicely.

Final Answer:
The curved surface area of the cone is 550 cm2.