Volume of a combination of solids
- CBSE · NCERT Class 10, Ch 12 Surface Areas and Volumes
The volume of a combination of solids is the space it fills, found by adding the volumes of its parts or taking away a part that was removed.
Volume works more simply than surface area. Nothing is hidden when solids are joined, so the volumes just add. When a shape is cut out of a solid, its volume is taken away. First, name each basic solid: cuboid, cone, cylinder, sphere or hemisphere.
A small example
A toy is a cone of radius 3 cm and height 4 cm on top of a hemisphere of the same radius. The cone's volume is 1/3 × π × 3² × 4 = 12π cm³. The hemisphere's volume is 2/3 × π × 3³ = 18π cm³. The toy's volume is 12π + 18π = 30π cm³.
Where marks go
Question 34 of CBSE's 2026-27 Maths Basic sample paper has a hemisphere drilled out of a wooden cube of side 21 cm. Part (i) asks for the wood left. The 2026-27 Maths Basic marking scheme gives half a mark for the radius, 21/2 cm. It gives half a mark for writing the plan: cube minus hemisphere.
Putting in the numbers earns 1 mark, and the answer, 6835.5 cm³, earns the last half. The plan line earns its mark before any arithmetic. This is step marking in a volume question.
Sources
Facts last checked against these sources on 30 September 2026.
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