MH Police Bharti · Bite-size lessons
Area & Volume
About 6 min · Mathematics · English
Time worked out from the lesson's 371 words at 150 words a minute, plus a minute for each question.
Area and Volume is a topic in Maharashtra Police Bharti Mathematics. Questions may ask you to calculate the surface area or volume of basic 3-D shapes — cube, cuboid, sphere, cylinder, cone or hemisphere. Mastering 8–10 formulas and understanding when to apply each is the key to solving these problems quickly.
Key ideas
- Surface Area measures the total outer covering of a 3-D object — think of how much paint is needed. Measured in square units (cm², m²).
- Volume measures the space inside a 3-D object — think of how much water it can hold. Measured in cubic units (cm³, m³).
- Lateral/Curved Surface Area (LSA/CSA) excludes the top and bottom faces. Use this when a container is open or when only the sides are painted.
- Total Surface Area (TSA) includes all faces — top, bottom, and sides.
- 1 litre = 1000 cm³ = 0.001 m³ — This conversion appears in almost every tank/container problem.
Watch out for
- Confusing LSA with TSA → LSA excludes top/bottom; TSA includes all faces. Read the question: "walls only" = LSA, "entire surface" = TSA.
- Forgetting to square or cube the radius → In πr²h, the radius is squared. In (4/3)πr³, it is cubed. Write formulas carefully.
- Mixing radius and diameter → Questions often give diameter. Always halve it to get radius before applying formulas.
Quick reference
- Cube: V = a³, TSA = 6a², Diagonal = a√3
- Cuboid: V = lbh, TSA = 2(lb + bh + hl), LSA = 2h(l + b)
- Cylinder: V = πr²h, CSA = 2πrh, TSA = 2πr(r + h)
- Sphere: V = (4/3)πr³, SA = 4πr²
- 1 m³ = 1000 litres = 10⁶ cm³
Check yourself: 3 questions
1. A cubical water tank has an edge of 5 meters. What is the volume of water it can hold in cubic meters?
2. A closed cylindrical drum has radius 7 cm and height 10 cm. What is its total surface area in square cm? (Use π = 22/7)
3. A solid sphere has a radius of 21 cm. What is its volume in cubic cm? (Use π = 22/7)
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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