Volume Aqa Foundation

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

  • 

  • 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

  • 

  • This formula is not 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

  • 

  • This formula is not given to you in the exam

• Note that a cylinder is similar to a prism, its cross-section is a circle with area <img alt=”pi italic space r squared” data-mathml='<math ><semantics><mrow><mi>&#960;</mi><mo mathvariant=”italic”>&#160;</mo><msup><mi>r</mi><mn>2</mn></msup></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”23″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2223%22%20width%3D%2231%22%20wrs%3Abaseline%3D%2217%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3E%26%23x3C0%3B%3C%2Fmi%3E%3Cmo%20mathvariant%3D%22italic%22%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1437d7d1d97917cd627a34a6a0f’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAt2hlYWQQC2qxAAACRAAAADZoaGVhCGsXSAAAAnwAAAAkaG10eE2rRkcAAAKgAAAACGxvY2EAHTwYAAACqAAAAAxtYXhwBT0FPgAAArQAAAAgbmFtZaBxlY4AAALUAAABn3Bvc3QB9wD6AAAEdAAAACBwcmVwa1uragAABJQAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAA8D%2F%2FwAAA8D%2F%2F%2FxBAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABAFUAAALAAkAAGQBBGAGwGhCwDdSwDRCwB9SwBxCwBNSwBBCwGNQAsBoQsAvUsBoQsALUsBoQsA%2FUsA8QsBTUsA8