Surface Areas and Volumes PYQs
Revise combinations and conversions of solids through stepwise Class 10 board questions.
Use these questions to select the right surface-area or volume formula for cylinders, cones, spheres, and hemispheres. Pay attention to composite diagrams, unit conversions, and conserved volume when a solid is melted, recast, or reshaped.
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CBSE Board Exam Blueprint & Topic Weightage: Surface Areas and Volumes
In the Class 10 CBSE Board Examination, Surface Areas and Volumes is a high-yielding component of Unit 6: Mensuration, consistently carrying 5 to 6 marks in the annual 80-mark written board paper. Recurring question formats observed over past board papers include:
- Section A (1 Mark MCQ): Ratio of volumes of two spheres, surface area of hemisphere, or slant height of cone \(l = \sqrt{r^2+h^2}\).
- Section C (3 Marks): Total surface area and volume of combined solids (e.g. test tube consisting of cylinder surmounted by hemisphere, toy in form of cone mounted on hemisphere).
- Section D / E (4 to 5 Marks): Conversion of one solid shape into another (melting metallic spheres into a cylinder where volume remains constant) and water flow rate problems through cylindrical pipes into tanks.
Key Revision Tips & Common Pitfalls
When two solids are joined (such as a cylinder and hemisphere), remember that the joined circular base is internal, so Total Surface Area is \(\text{CSA of cylinder} + \text{CSA of hemisphere}\), NOT the sum of their individual total surface areas. Keep \(\pi\) in common factor calculations to simplify arithmetic.