Practice Surface area and volume of solids
Volume measures the three-dimensional space inside a solid using cubic units.
Choose a formula that matches the shape and convert all lengths to compatible units.
Exercises with solutions
Sphere, cylinder and cone have fixed formulas. Cylinder: V = π · r² · h. Cone: V = (1/3) · π · r² · h. Sphere: V = (4/3) · π · r³. Using π ≈ 3.14 gives an approximate value.
Exercise 1
A cylinder has r = 3 cm and h = 10 cm. Calculate the volume.
Show solution and working
about 282.6 cm³
V = π · r² · h = 3.14 · 9 cm² · 10 cm = 282.6 cm³.
Exercise 2
A cone has r = 3 cm and h = 10 cm. Calculate the volume.
Show solution and working
about 94.2 cm³
A cone is one third of the cylinder with the same radius and height: 282.6 ÷ 3 = 94.2 cm³.
Exercise 3
A sphere has r = 3 cm. Calculate the volume.
Show solution and working
about 113.04 cm³
V = (4/3) · π · r³ = (4/3) · 3.14 · 27 cm³ = 113.04 cm³.
Exercise 4
How does the volume of a cylinder change when you double the radius?
Show solution and working
it becomes four times as large
The radius enters the formula squared. With double the radius r² becomes four times as large, and so does the volume.
Common mistake
Confusing radius and diameter — every formula needs the radius. And forgetting the factor 1/3 for the cone, since a cone is only one third of the cylinder.
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