ICSE Class 10 Mathematics: Mensuration — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: Find the volume and surface area of a cylinder with radius 7 cm and height 10 cm.
  Ans: Volume = πr²h = (22/7)(7²)(10) = (22/7)(49)(10) = 1540 cm³. Curved Surface Area = 2πrh = 2(22/7)(7)(10) = 440 cm². Total Surface Area = 2πr(r+h) = 2(22/7)(7)(17) = 748 cm².
• Q: A cone has radius 5 cm and slant height 13 cm. Find its volume.
  Ans: Height h = √(l² - r²) = √(169 - 25) = √144 = 12 cm. Volume = (1/3)πr²h = (1/3)(22/7)(25)(12) = (1/3)(22/7)(300) = 2200/7 ≈ 314.3 cm³.
• Q: A hemisphere has radius 14 cm. Find its volume and total surface area.
  Ans: Volume = (2/3)πr³ = (2/3)(22/7)(14)³ = (2/3)(22/7)(2744) = 5749.3 cm³. Total Surface Area = 3πr² = 3(22/7)(196) = 1848 cm².

Long Answer / Application Questions (4-6 Marks)

• Q: A solid is in the shape of a cone surmounted on a hemisphere. The radius is 3.5 cm and total height is 9.5 cm. Find the volume.
  Ans: Height of cone = total height - radius = 9.5 - 3.5 = 6 cm. Volume of cone = (1/3)(22/7)(3.5)²(6) = (1/3)(22/7)(12.25)(6) = 77 cm³. Volume of hemisphere = (2/3)(22/7)(3.5)³ = (2/3)(22/7)(42.875) = 89.83 cm³. Total volume = 77 + 89.83 = 166.83 cm³.

Exam Tips for This Chapter

• Revise all definitions and laws from Mensuration — they are commonly asked as 1-2 mark questions
• Practice diagrams related to Mensuration — neat labelled diagrams carry 2-3 marks
• For numericals, always show formula → substitution → answer with correct units
• Previous year analysis shows Mensuration carries 8-12 marks in the board exam