Advanced problem solving with further surface area and volume
I can use my enhanced knowledge of surface area and volume to solve problems.
Advanced problem solving with further surface area and volume
I can use my enhanced knowledge of surface area and volume to solve problems.
Lesson details
Key learning points
- The surface area of any solid can be calculated by a known method.
- The volume of any solid can be calculated by a known method.
- Writing an algebraic statement about surface area/volume can be done from a diagram.
Common misconception
When questions are in context, the length may be described as the depth or height and this can cause some pupils to struggle if they have learned a formula with a particular word.
Remind pupils that the volume of a 3D shape comes from a product of three perpendicular lengths. They may need to evaluate a perpendicular length from other given information, using trigonometry or Pythagoras' theorem.
Keywords
Volume - The volume is the amount of space occupied by a closed 3D shape.
Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
Loading...
Starter quiz
6 Questions
Volume of hemisphere -
$$\frac{2}{3} \pi r^3$$
Volume of cone -
$$\frac{1}{3}\pi r^2 h$$
Volume of cylinder -
$$ \pi r^2 h$$
Volume of pyramid -
$$\frac{1}{3}\times \text{area of base} \times \text {height}$$
Volume of sphere -
$$\frac{4}{3} \pi r^3$$
Exit quiz
6 Questions
Surface area of a sphere -
$$2 \pi r^2$$
Volume of cylinder -
$$\pi r^2 h$$
Area of curved surface of cone -
$$\pi r l$$
Volume of sphere -
$$\frac{4}{3}\pi r^3$$
Curved surface area of cylinder -
$$2\pi r h$$
Volume of cone -
$$\frac{1}{3}\pi r^2h$$