Prisms
V = area of the base × height. From the cube (V = a³) and the cuboid (V = a × b × h) to triangular and regular hexagonal prisms, where the base area comes from the perimeter and the apothem.
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Teaching guide: how to practise the volume of solids
Volume measures the space a solid takes up. This free volume of solids worksheet generator builds A4 worksheets with every solid drawn in 3D, with dashed hidden edges and labelled lengths: prisms, pyramids, cylinders, cones, spheres and hemispheres, composite solids and capacity problems in litres. For Grades 8 and 9, with an answer key that writes the formula, the substitution and every calculation.
- For
- Middle & High 7th, 8th, 9th (ages 12-14)
- Subject
- Mathematics › Geometry & Measurement
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Pyramids and cones
They hold a third of the prism or cylinder with the same base and height. At level 3 the height comes from Pythagoras' theorem and the slant height.
Cylinders and spheres
V = π × r² × h and V = (4 × π × r³) ÷ 3. Given the diameter, halve it first; at level 3 pupils work back from the volume to the radius or the height.
π = 3.14 or in terms of π
Choose whether answers use π = 3.14 or are left in terms of π (12π cm³). The lengths are chosen so that every calculation is exact either way.
Composite solids
A house, a rocket, a silo or an ice cream: split the solid into known pieces and add their volumes; when it has a hole, subtract it.
Capacity problems
Fish tanks, pools, cans and water tanks: volumes become litres (1 dm³ = 1 L) and, at level 3, pupils find how deep the water is or how long a pool takes to fill.
Frequently asked questions about volume worksheets
Which grade learns the volume of solids?
Grade 8 (Year 9) covers the volume of prisms, pyramids, cylinders, cones and spheres. In Grade 9 volume is used with Pythagoras' theorem and in problems that work back from the volume; level 3 of each type follows that order.
What is the volume formula of each solid?
Prism and cylinder: area of the base × height. Pyramid and cone: a third of the area of the base × height. Sphere: (4 × π × r³) ÷ 3. You can print the formula under each instruction.
Which value of π do the worksheets use?
π = 3.14 by default, and the instruction says so. For cylinders, cones and spheres you can also ask for answers in terms of π (for example 36π cm³). Lengths are chosen so that the answers are exact.
How are the solids drawn?
In 3D, seen from above and to the side, with dashed hidden edges and lengths labelled with letters; their values are written next to the drawing.
What is in the answer key?
Every step: the formula, the area of the base, the lengths substituted, the calculations and the answer with its unit. For composite solids, the volume of each piece; for problems, the conversion to litres.
How do you turn volume into capacity?
1 dm³ is 1 litre, 1 cm³ is 1 millilitre and 1 m³ is 1000 litres. The level 1 problems practise it with fish tanks and swimming pools.
What other worksheets go well with these?
The area and perimeter worksheets for the areas of the bases, the Pythagorean theorem worksheets for heights and slant heights, and the metric units worksheets to convert cm³ to litres. Find every resource under maths worksheets.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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