CBSE Class 10 Mathematics: Surface Areas and Volumes — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: A solid is in the shape of a cone mounted on a hemisphere. The radius is 3 cm and height of cone is 4 cm. Find the total surface area.
  Ans: Slant height of cone l = √(r² + h²) = √(9 + 16) = √25 = 5 cm. CSA of cone = πrl = π(3)(5) = 15π cm². CSA of hemisphere = 2πr² = 2π(9) = 18π cm². Total surface area = 15π + 18π = 33π = 33 × 22/7 ≈ 103.71 cm².
• Q: A metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm. Find the height of the cylinder.
  Ans: Volume of sphere = Volume of cylinder (metal is conserved). (4/3)πr₁³ = πr₂²h. (4/3)(4.2)³ = (6)²h. (4/3)(74.088) = 36h. 98.784 = 36h. h = 2.744 cm.
• Q: Water flows through a cylindrical pipe of radius 7 cm at 5 m/s. Find the time to fill a tank of 5.5 m³.
  Ans: Volume of water per second = πr²v = (22/7)(0.07)²(5) = (22/7)(0.0049)(5) = 0.077 m³/s. Time = Volume of tank / Rate = 5.5/0.077 = 71.4 seconds ≈ 1 min 11.4 s.

Exam Tips for This Chapter

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