Use surface-area and volume formulae for cubes, cuboids, cylinders, cones, spheres and hemispheres, including combinations of two solids.
Use surface-area and volume formulae for cubes, cuboids, cylinders, cones, spheres and hemispheres, including combinations of two solids.
For a joined solid, do not count the hidden common face. Add only the exposed curved and flat surfaces requested. Volume is additive when solids are joined and subtractive when a cavity is removed.
Area uses square units and volume uses cubic units. Convert all lengths to the same unit before calculation. For a cone, find slant height with Pythagoras when it is not given.
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Question: A toy is a cone of radius 3 cm and height 4 cm joined to a cylinder of the same radius and height 10 cm. Find volume and exposed area.
Solution: Cone slant height=5 cm. Volume=(1/3)π(9)(4)+π(9)(10)=12π+90π=102π cm³. Exposed area=cone CSA 15π + cylinder CSA 60π + bottom base 9π =84π cm²; the joined circle is hidden.
Question: A sphere of radius 3 cm is melted into smaller spheres of radius 1 cm. How many are formed?
Solution: Volume ratio=(4/3π·3³)/(4/3π·1³)=27. Therefore 27 smaller spheres are formed.
Measure a cylindrical can and a cone-shaped paper cup. Estimate capacity using V=πr²h and V=⅓πr²h; compare with water displacement or a measuring cup. Discuss why a cone with the same base and height holds one-third the cylinder’s volume.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Try each question before opening its solution.
V=⅓π×9×4=12π cm³.
CSA=2πr²=98π=308 cm² using π=22/7.
Cylinder=20π; hemisphere=16π/3; total=76π/3 cm³.
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.