Practice tests · TNPSC

TNPSC area and volume practice questions with formulas

By the PrepMatic team · Updated 9 Oct 2026 · 3 min read

Area and volume questions in the TNPSC aptitude section test whether you know about twelve formulas and can apply them without unit mistakes. They rarely require long calculation, but they punish one slip, such as using the diameter for the radius or forgetting to convert cubic metres to litres. The five questions below are typical SSLC-level mensuration. TNPSC aptitude and mental ability covers the subject in full.

What this topic covers

• Plane figures: rectangle, square, triangle, parallelogram, trapezium and circle.
• Solids: cube, cuboid, cylinder, cone and sphere.
• Practical problems: cost of fencing or carpeting, capacity of tanks, and unit conversions.

Take π = 22/7 when the radius or diameter is a multiple of 7, which is the standard TNPSC convention. Remember that 1 cubic metre equals 1,000 litres.

Sample questions

Question 1

The area of a triangle with base 12 cm and height 9 cm is:

• A. 54 cm²
• B. 108 cm²
• C. 21 cm²
• D. 72 cm²

Question 2

The area of a circle of radius 14 cm is (take π = 22/7):

• A. 44 cm²
• B. 88 cm²
• C. 308 cm²
• D. 616 cm²

Question 3

A tank is 3 m long, 2 m wide and 1.5 m deep. How many litres of water can it hold?

• A. 900
• B. 9,000
• C. 90,000
• D. 6,500

Question 4

The volume of a cylinder of radius 7 cm and height 10 cm is (take π = 22/7):

• A. 440 cm³
• B. 770 cm³
• C. 1,540 cm³
• D. 1,078 cm³

Question 5

A square field has an area of 900 m². The cost of fencing it at ₹10 per metre is:

• A. ₹900
• B. ₹1,800
• C. ₹3,600
• D. ₹1,200

Answers and explanations

1. A. Area = ½ × 12 × 9 = 54 cm². The answer 108 comes from forgetting the half.
2. D. Area = πr² = 22/7 × 14 × 14 = 22 × 2 × 14 = 616 cm². The value 88 would be the circumference 2πr.
3. B. Volume = 3 × 2 × 1.5 = 9 m³. Since 1 m³ is 1,000 litres, the tank holds 9,000 litres.
4. C. Volume = πr²h = 22/7 × 7 × 7 × 10 = 22 × 7 × 10 = 1,540 cm³.
5. D. Side = √900 = 30 m, so the perimeter is 4 × 30 = 120 m. The cost is 120 × 10 = ₹1,200. Area is not needed for the cost of fencing, only the perimeter.

How to prepare area and volume

Put the formula table on one page and rewrite it from memory every day for a week. Twelve formulas are a small load, and the habit is what matters. Add three conversions at the bottom: 1 m = 100 cm, 1 m³ = 1,000 litres, and 1 hectare = 10,000 m².

Then practise reading the question for what it actually asks. Fencing needs perimeter, painting and carpeting need area, and filling needs volume. Many wrong answers in this chapter come from computing the right number for the wrong quantity.

Build the habit of writing units. If the radius is in centimetres, area is in square centimetres and volume is in cubic centimetres. When the question mixes metres and centimetres, convert everything to one unit before you multiply.

For quick calculation with fractions and decimals in these formulas, see TNPSC simplification practice, and for percentage questions that use areas, such as "length increased by 10%", see TNPSC percentage practice.

Take the full topic test on PrepMatic

Aptitude topics like area and volume are quick to test in short rounds. A PrepMatic topic test runs about 15 questions in 30 minutes, and after you take a few, your analytics show whether you are losing time or accuracy. If you write the exam in Tamil, choose Tamil as your exam language so you practise the terms you will meet on the day.

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