A cylinder of radius 4.3 cm and height 4.8 cm is melted and recast into a right circular cone having the same radius as the cylinder. What will be the height of this cone? (Use π = 22/7.)

Introduction / Context:
This question involves conservation of volume when a solid is melted and recast into another shape. Here a cylinder is melted to form a cone, and you are required to find the new height. Such questions are common in quantitative aptitude, because they require you to apply volume formulas and to recognise that total volume of material remains constant during the transformation.

Given Data / Assumptions:

• Radius of the cylinder, r_cyl = 4.3 cm.
• Height of the cylinder, h_cyl = 4.8 cm.
• The cylinder is melted and recast into a cone.
• The cone has the same radius as the cylinder, r_cone = 4.3 cm.
• Height of the cone, h_cone, is unknown.
• Use π = 22/7 and assume no loss of material during melting and recasting.

Concept / Approach:
The volumes of the original and the recast solid must be equal. The volume of a cylinder is:
V_cylinder = π * r_cyl^2 * h_cyl. The volume of a cone is:
V_cone = (1 / 3) * π * r_cone^2 * h_cone. Since r_cyl = r_cone, the radius cancels nicely when we equate the two volumes. This makes it straightforward to isolate and calculate h_cone.

Step-by-Step Solution:
Step 1: Write the cylinder volume: V_cylinder = π * r_cyl^2 * h_cyl. Step 2: Substitute r_cyl = 4.3 and h_cyl = 4.8: V_cylinder = π * (4.3)^2 * 4.8. Step 3: Write the cone volume: V_cone = (1 / 3) * π * r_cone^2 * h_cone. Step 4: Since r_cone = 4.3, V_cone = (1 / 3) * π * (4.3)^2 * h_cone. Step 5: Equate volumes: π * (4.3)^2 * 4.8 = (1 / 3) * π * (4.3)^2 * h_cone. Step 6: Cancel π and (4.3)^2 from both sides: 4.8 = (1 / 3) * h_cone. Step 7: Multiply both sides by 3: h_cone = 3 * 4.8 = 14.4 cm. Step 8: Match this with the options: 14.4 cm is available and is therefore the correct choice.

Verification / Alternative check:
We can verify by computing approximate numerical volumes. The cylinder volume is π * (4.3)^2 * 4.8 and the cone volume with h_cone = 14.4 is (1 / 3) * π * (4.3)^2 * 14.4. Since 14.4 / 3 = 4.8, the cone volume simplifies back to π * (4.3)^2 * 4.8, exactly matching the cylinder volume. This confirms that our reasoning and arithmetic are correct.

Why Other Options Are Wrong:
A height of 28.8 cm or 21.6 cm would produce a cone with volume larger than the original cylinder, which is impossible without adding material. Heights of 7.2 cm or 10.8 cm would yield smaller volumes than the original cylinder, meaning that some material would have disappeared. Only 14.4 cm gives a cone with the same volume as the cylinder, which is required by the melting and recasting process.

Common Pitfalls:
One typical mistake is to forget the factor of 1 / 3 in the cone volume formula, leading to incorrect proportionality between the heights. Another error is to square the radius incorrectly or to cancel the π factor prematurely without considering the rest of the expression. Some students also try to relate heights directly using simple ratios, but the correct relationship comes from equating full volume expressions, not from intuitive height comparisons.

Final Answer:
Therefore, the height of the recast cone is 14.4 cm.