Volume

Volumevideo

Volume

What is volume?

• The volume of a 3D shape is a measure of how much space it takes up

• You need to be able to calculate the volumes of a number of common 3D shapes, including:

  • Cubes and cuboids

  • Prisms

  • Pyramids

  • Cylinders

  • Spheres

How do I find the volume of a cube or a cuboid?

• A cube is a special cuboid, where the length, width and height are all of equal length

• A cuboid is another name for a rectangular-based prism

• To find the volume, V, of a cube or a cuboid, with length, l, width, w, and height, h, use the formula

  • $V=lwh$

  • This formula is not given to you in the exam

• You will sometimes see the terms  'depth' or 'breadth' instead of 'height' or 'width'

How do I find the volume of a prism?

• A prism is a 3D object with a constant cross-sectional area

• To find the volume, V, of a prism, with cross-sectional area, A, and length, l, use the formula

  • $V=Al$

  • This formula is given to you in the exam

• Note that the cross-section can be any shape, so as long as you know its area and the length of the prism, you can calculate its volume

  • If you know the volume and length of the prism, you can calculate the area of the cross-section

How do I find the volume of a cylinder?

• To calculate the volume, V, of a cylinder with radius, r, and height, h, use the formula

  • $V=\pi \mathit{ }{r}^{2}h$

  • This formula is given to you in the exam

• Note that a cylinder is similar to a prism, its cross-section is a circle with area $\pi \mathit{ }{r}^2$, and its length is h

How do I find the volume of a pyramid?

• To calculate the volume, V, of a pyramid with base area, A, and perpendicular height, h, use the formula

  • $V=\frac{1}{3}Ah$

  • This formula is given to you in the exam

• The height must be a line from the top of the pyramid that is perpendicular to the base

• The base of a pyramid could be a square, a rectangle or a triangle

How do I find the volume of a cone?

• To calculate the volume, V, of a cone with base radius, r, and perpendicular height, h, use the formula

  • $V=\frac{1}{3}\pi \mathit{ }{r}^{\mathit{2}}h$

  • This formula is given to you in the exam

• Note that volume formula for a cone is similar to a pyramid

• The height must be a line from the top of the cone that is perpendicular to the base

How do I find the volume of a sphere?

• To calculate the volume, V, of a sphere with radius, r, use the formula

  • $V=\frac{4}{3}\pi \mathit{ }{r}^3$

  • This formula is given to you in your exam