MathsICSE Class 8 · Surface Area and Volume

Volume, Capacity and Recasting of Solids (ICSE Class 8 Maths)

Updated 17 October 2026 · Fact-checked

Volume of a cuboid $= lbh$, cube $= a^3$, cylinder $= \pi r^2 h$. Capacity is the volume of liquid a container holds: $1\text{ litre} = 1000\text{ cm}^3$ and $1\text{ m}^3 = 1000$ litres. When a solid is melted and recast, or immersed in water, volume is conserved.

The shape changes when a solid is melted and recast, but its volume does not, so set the old formula equal to the new one.

Illustration drawn for QuestionBuddy.

Understand Volume, Capacity and Recasting

The CISCE curriculum covers the concept of volume, measuring volume with a basic unit, volume of a cube, cuboid and cylinder, and volume and capacity.

Volume formulas. Cuboid $V = l bh$ ; cube $V = a^{3}$ ; cylinder $V = π r^{2} h$ . A cuboid's volume counts how many unit cubes fit: $l \times b \times h$ layers.

Units of capacity. $1 cm^{3} = 1 mL$ , $1 L = 1000 cm^{3}$ , $1 m^{3} = 1000 L$ . Convert units before computing.

Finding a missing dimension. Divide: depth $=$ volume $\div$ base area; for a cylinder, $r^{2} = \frac{V}{π h}$ .

Recasting (melting). Volume does not change when a solid is melted and recast: $V_{old} = V_{new}$ . The number of small cubes cut from a block is $\frac{volume of block}{volume of one cube}$ .

Pouring and immersion. When liquid is poured from a cylinder to a cuboid tank, equate volumes and find the rise as $rise = \frac{V}{base area}$ . A solid fully immersed in water raises the level by $\frac{volume of solid}{base area of tank}$ (no overflow).

Sanity check. Volumes are in cubic units; capacities in litres or mL after conversion.

Volume, Capacity and Recasting: formulas to remember

Volumes: $V_{c u b o i d} = l bh, V_{c u b e} = a^{3}, V_{cy l} = π r^{2} h$; Cubic units.
Capacity conversion: $1 L = 1000 cm^{3}, 1 m^{3} = 1000 L$; $1 cm^{3} = 1 mL$ .
Level rise: $rise = \frac{volume added}{base area}$; For tanks with straight sides.

How to solve Volume, Capacity and Recasting questions

Compute volumes in consistent units, then equate volumes for recasting, pouring and immersion.

1Write the volume formula for each solid.
2Convert all dimensions to one unit.
3Compute each volume.
4Equate volumes for melting, pouring or immersion.
5Convert to litres when asked for capacity.

Volume, Capacity and Recasting in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Filling a tank

Suppose a water tank is 2 m long, 1.5 m wide and 1 m deep.

How many litres does it hold when full?

Try it first, then show the solutionSolution

Volume $= 2 \times 1.5 \times 1 = 3$ m $^{3}$ .
Capacity $= 3 \times 1000 = 3000$ litres.

Answer: 3000 litres.

Memory hook: One cubic metre is a thousand litres.

Tricks to remember Volume, Capacity and Recasting

Short memory aids. Say each one aloud once, then use it on a question the same day.

Volume in, litre out
Volume in cm³ divided by 1000 gives litres.
Use it when: Capacity conversion.
Volume conserved
Melting or pouring keeps volume the same; only the shape changes.
Use it when: Recasting problems.

Volume, Capacity and Recasting: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Volume of a cuboid · 1 mark · MCQBoard level

The volume of a cuboid 10 cm by 6 cm by 4 cm is:
(a) 20 cm $^{3}$ (b) 240 cm $^{3}$ (c) 120 cm $^{3}$ (d) 480 cm $^{3}$

Try it first, then show the solutionSolution

$10 \times 6 \times 4 = 240$ .

Answer: (b)

Example 2: Capacity in litres · 3 marks · Short answerBoard level

A water tank is 2 m long, 1.5 m wide and 1 m deep. How many litres can it hold?

Try it first, then show the solutionSolution

$V = 2 \times 1.5 \times 1 = 3$ m $^{3}$ .
$3 \times 1000 = 3000$ litres.

Answer: 3000 litres

Example 3: Volume of a cylinder · 3 marks · Short answerHarder board level

A cylinder has radius 7 cm and height 15 cm. Find its volume, and its capacity in litres.

Try it first, then show the solutionSolution

$V = \frac{22}{7} \times 49 \times 15 = 2310$ cm $^{3}$ .
Capacity $= \frac{2310}{1000} = 2.31$ litres.

Answer: 2310 cm $^{3}$ ; 2.31 L

Example 4: Cutting a block into cubes · 4 marks · Short answerHarder board level

A metal block 50 cm by 40 cm by 30 cm is melted and recast into cubes of edge 10 cm. How many cubes are formed?

Try it first, then show the solutionSolution

Block volume $= 50 \times 40 \times 30 = 60000$ cm $^{3}$ .
Cube volume $= 1000$ cm $^{3}$ .
Number $= 60000 \div 1000 = 60$ .

Answer: 60 cubes

Example 5: Immersing cubes in water · 4 marks · Case-basedHOTS / competency

A tank has a base of 40 cm by 25 cm and contains water 12 cm deep. (i) Find the volume of water in litres. (ii) A solid metal cube of edge 10 cm is fully immersed; find the new depth. (iii) How many such cubes can be immersed before the depth reaches 20 cm?

Try it first, then show the solutionSolution

(i) $40 \times 25 \times 12 = 12000$ cm $^{3}$ $= 12$ L.
(ii) Cube volume $= 1000$ ; base area $= 1000$ ; rise $= 1$ cm; new depth $13$ cm.
(iii) Each cube raises the level by $1$ cm, so $20 - 12 = 8$ cubes (they fit: $4 \times 2 = 8$ on the base).

Answer: 12 L; 13 cm; 8 cubes

Where students lose marks in Volume, Capacity and Recasting

The slips examiners see most often, and what to write instead.

Mistake: Dividing by 100 instead of 1000 for litres
A litre is 1000 cm³.
Wrong working
$2310$ cm $^{3}$ $= 23.1$ L.
Right working
$2.31$ L.
Do this: Write the conversion factor with units.
Usually costs: Answer mark.
Mistake: Mixing units in the volume
All lengths must be in one unit.
Wrong working
$2$ m $\times 150$ cm $\times 1$ m.
Right working
$2 \times 1.5 \times 1 = 3$ m $^{3}$ .
Do this: Convert first.
Usually costs: Answer mark.

Exam tips

Write the unit of each length and convert before multiplying.
For recasting say "volume of the old solid = volume of the new solid".
Round only at the end.

Practice questions on Volume, Capacity and Recasting

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
One litre is equal to:
(a) 10 cm $^{3}$ (b) 100 cm $^{3}$ (c) 1000 cm $^{3}$ (d) 10000 cm $^{3}$
Hint
Remember mL = cm^3.
Answer
(c)
Q2 · 2 marks · Short answerBoard level
Find the volume of a cube of side 15 cm in cm $^{3}$ and in litres.
Hint
a cubed.
Answer
$1 5^{3} = 3375$ cm $^{3}$ $= 3.375$ L.
Q3 · 3 marks · Short answerHarder board level
A rectangular tank with a base area of 2.5 m $^{2}$ must hold 3750 litres. Find its depth.
Hint
Convert litres to cubic metres first.
Answer
$3750$ L $= 3.75$ m $^{3}$ . Depth $= \frac{3.75}{2.5} = 1.5$ m.
Q4 · 3 marks · Short answerHarder board level
A cylinder of height 10 cm has volume 1540 cm $^{3}$ . Find its radius.
Hint
r squared = V/(pi h).
Answer
$r^{2} = \frac{1540}{\frac{22}{7} \times 10} = 49$ , so $r = 7$ cm.
Q5 · 4 marks · Long answerHOTS / competency
A cylindrical bucket of radius 14 cm and height 20 cm full of water is emptied into a rectangular tank with base 44 cm by 28 cm. Find the rise in the water level.
Hint
Equate volumes.
Answer
Bucket volume $= \frac{22}{7} \times 196 \times 20 = 12320$ cm $^{3}$ . Base area $= 44 \times 28 = 1232$ cm $^{2}$ . Rise $= \frac{12320}{1232} = 10$ cm.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Volume of a cylinder?Show answer
pi r^2 h.
2.1 m^3 in litres?Show answer
1000 L.
3.Number of cubes from a block?Show answer
Volume of block divided by volume of one cube.
4.Rise of water when a solid is immersed?Show answer
Volume of solid divided by base area.

Volume, Capacity and Recasting: frequently asked questions

Is capacity the same as volume?

Capacity is the volume of liquid the container can hold, usually measured in litres or mL.

Does melting change volume?

No; volume stays the same.