The volume of a right circular cylinder is 3850 cubic centimetres and its height is 25 cm. Taking π = 22/7, what is the radius of its base (in cm)?

Introduction / Context:
This question focuses on using the volume formula for a right circular cylinder. We are given the volume and the height and asked to find the radius of the base. This type of problem is very common in quantitative aptitude tests and helps reinforce how to rearrange formulas and substitute numerical values correctly, especially when using a specific approximation for π such as 22/7.

Given Data / Assumptions:
• Volume of the cylinder, V, is 3850 cubic centimetres.
• Height (or length) of the cylinder, h, is 25 cm.
• π is to be taken as 22/7.
• Radius of the base, r, is unknown and needs to be found.

Concept / Approach:
The volume of a right circular cylinder is given by V = πr²h. Here V and h are known, and π is specified, so we can rearrange the formula to r² = V / (πh). After computing r², we take the square root to find r. The data are chosen so that r² becomes a neat perfect square, making the result an integer. Careful handling of fractions is important to get the correct value for r.

Step-by-Step Solution:
Step 1: Start with the cylinder volume formula: V = πr²h. Step 2: Substitute the given values V = 3850, h = 25, and π = 22/7. Step 3: We get 3850 = (22/7) * r² * 25. Step 4: Combine constants: (22/7) * 25 = 550 / 7, so 3850 = (550 / 7) * r². Step 5: Rearrange to solve for r²: r² = 3850 * (7 / 550). Step 6: Simplify the fraction: 3850 / 550 = 7, so r² = 7 * 7 = 49. Step 7: Take the square root: r = √49 = 7 cm.

Verification / Alternative check:
We can verify by substituting r = 7 cm back into the volume formula. Then V = πr²h = (22/7) * 7² * 25. Here 7² = 49, so V = (22/7) * 49 * 25. First, 49 / 7 = 7, giving V = 22 * 7 * 25. Then 22 * 7 = 154, and 154 * 25 = 3850. This matches the given volume exactly, confirming that the radius is 7 cm. Any other assumed radius would change r² and lead to a different volume, so the answer is unique and correct.

Why Other Options Are Wrong:
5 cm and 6 cm produce r² values of 25 and 36 respectively, which lead to volumes smaller than 3850 cubic centimetres when substituted into V = πr²h.
8 cm and 9 cm generate r² values of 64 and 81, which lead to volumes greater than 3850 cubic centimetres. None of these match the required volume, so they are incorrect.

Common Pitfalls:
Typical mistakes include forgetting to multiply all constants correctly when combining π and the height, or incorrectly simplifying the fraction 3850 * 7 / 550. Some learners also forget to take the square root after obtaining r², or miscalculate that square root. Writing the working clearly and simplifying step by step makes it easier to avoid such errors.

Final Answer:
The radius of the cylinder is 7 cm.