Volume and surface area · Grade 9
In Grade 9 you learn: cones, pyramids and spheres.
Volume is how much space a solid takes up, measured in cubic units; surface area is the total area of all its faces. For any prism (including cuboids and cylinders) the volume is the area of the cross-section times the length.
Key facts
- Cuboid: V = length × width × height.
- Any prism: V = area of cross-section × length.
- Cylinder: V = πr²h; curved surface = 2πrh; total surface = 2πr² + 2πrh.
- Surface area: add the areas of all the faces (a net helps).
- 1 litre = 1,000 cm³, and 1 cm³ holds 1 ml.
Worked examples
Example 1
A cuboid is 6 cm long, 5 cm deep and 4 cm tall. Find its volume and its surface area.
Answer: Volume 120 cm³, surface area 148 cm²
Example 2
A cylinder has radius 3 cm and height 10 cm. Find its volume, to 1 d.p.
Answer: 282.7 cm³