The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Solids – worksheets to print
Cylinder, cone, pyramid and sphere: work out volume, lateral area and surface area, work back from the volume to the height or radius, and composite solids.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Solids: explained simply
Cylinders, cones, pyramids and spheres are solids. The volume tells you how much fits inside, the surface area how much material the outside needs.
How to work it out
- Cylinder: V = π · r² · h. Pointed solids (cone, pyramid) hold a third of that: V = ⅓ · B · h.
- Sphere: V = ⁴⁄₃ · π · r³ and A = 4 · π · r².
- Surface area = base(s) + lateral surface. Cylinder: L = 2 · π · r · h, cone: L = π · r · s with the slant height s.
An example, step by step
A cylinder has r = 3 cm and h = 10 cm. Find its volume using π ≈ 3.14.
- Base: B = 3.14 · 3² = 3.14 · 9 = 28.26 cm².
- Volume: V = B · h = 28.26 cm² · 10 cm.
- V = 282.6 cm³.
Understand other variations
Surface area
The same cylinder: A = 2 · 3.14 · 3² + 2 · 3.14 · 3 · 10 = 56.52 + 188.4 = 244.92 cm².
Working backwards
A cylinder with r = 5 cm holds 785 cm³. B = 3.14 · 25 = 78.5 cm², so h = 785 : 78.5 = 10 cm.
Composite solids
Split the solid into known parts, for example a silo into a cylinder and a hemisphere, and add the volumes. For a pipe, subtract the inner cylinder.
With a calculator
With the π key you work more precisely and round only at the end: π · 3² · 10 ≈ 282.74 cm³.
Your turn
Find the volume of a sphere with r = 3 cm (π ≈ 3.14).
Show the answer and method
V = ⁴⁄₃ · 3.14 · 3³ = ⁴⁄₃ · 3.14 · 27 = 3.14 · 36 = 113.04 cm³.
Ready-made worksheets: Solids
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