21. Mensuration: solids
Free study material · concepts, shortcuts & solved questions
Cuboid volume=lbh and total surface area=2(lb+bh+hl); cylinder volume=πr²h and curved surface area=2πrh; cone volume=1/3πr²h; sphere volume=4/3πr³ and surface area=4πr²; hemisphere volume=2/3πr³.
Method before formula Check whether the question asks curved or total surface area. Volume of a cone is one-third of the cylinder with the same base and height. Convert dimensions to one unit before calculating. |
Formula and decision table
Solid | Key formula |
Cuboid | V=lbh |
Cylinder | V=πr²h |
Cone | V=1/3πr²h |
Sphere | V=4/3πr³ |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
Cylinder r=7,h=10, π=22/7. Volume: | (22/7)×49×10=1540. | B. 1540 |
Cone volume compared with same cylinder: | Cone is one-third. | C. One-third |
Volume is measured in: | It is cubic. | C. m³ |
What an examiner is testing
The options around Mensuration: solids usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: Cylinder r=7,h=10, π=22/7. Volume: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 1540, because (22/7)×49×10=1540.
Example 2: Cone volume compared with same cylinder: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is One-third, because Cone is one-third.
Example 3: Volume is measured in: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is m³, because It is cubic.
Chapter practice
1. Cylinder r=7,h=10, π=22/7. Volume:
(A) 770 (B) 1540 (C) 3080 (D) 4400
Answer: B. 1540 | Explanation: (22/7)×49×10=1540.
2. Cone volume compared with same cylinder:
(A) Same (B) Half (C) One-third (D) Double
Answer: C. One-third | Explanation: Cone is one-third.
3. Volume is measured in:
(A) m (B) m² (C) m³ (D) degrees
Answer: C. m³ | Explanation: It is cubic.
SSC CGL speed and trap clinic
For Mensuration: solids, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Mensuration: solids? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Mensuration: solids question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |