Volume of cubes and cuboids Mathematics Volume of cubes and cuboids

Lesson Objectives The aim of this powerpoint is to help you… to learn and use the formulas for finding the volume of a cuboid to learn how to find the side length of a cube given the volume.

Dimensions REMEMBER: Perimeter is 1D (one dimension/distance) Area is a 2D (two perpendicular dimensions multiplied together) Volume is 3D (three perpendicular dimensions multiplied together) ADDING distances, areas or volumes together makes longer distances, bigger areas or bigger volumes You have to MULTIPLY dimensions or distances together to get areas or volumes

Measures REMEMBER: When calculating perimeters, areas and volumes, all dimensions must have the same type of units otherwise you will need to convert them first. You will need to recall… 1cm = 10mm 1m = 100cm (or 1m = 1000mm) 1km = 1000m

Volume of Cuboids Volume is 3-dimensional. You must multiply 3 perpendicular dimensions together. The volume of a cuboid (or cube) is its length × width × height (or depth) Formula: V = l × w × h width length depth

Volume of Cuboids Area is measured in squares – count them or calculate them but the measures are square-units. Volume is measured in cubes – count them or calculate them but the measures are cube-units. As area is already 2-dimensional, you can also calculate the volume of a cuboid (or cube) as the area of its end shape × height (or depth) V = A × h depth area height area

Working backwards… V V V lw h l wh lh w V A h V = lwh These formula triangles show that given the volume and any 2 dimensions, to find the third dimension you divide the volume by the product of the other two. V = Ah V V V lw h l wh lh w V A h This formula triangle shows that given the volume and the area of one face, to find the third dimension you divide the volume by the area.

Special case…Cube As a cube’s dimensions are all equal, the same distance is multiplied by itself three times, which is the definition of ‘cubing’. V = l × l × l so V = l³ To work backwards, you do the opposite of ‘cubing’. Therefore, if you know the volume of a cube, you can find the side-length by cube-rooting… l = ³ V

Quick Practice What are the volumes of these 3D shapes? CUBE CUBOID 12mm 25cm 1.5m 20cm

Solutions… Volume = length × length × length CUBE CUBOID Volume = length × width × height CUBE CUBOID 12mm 25cm 1.5m 20cm Volume = 12mm × 12mm × 12mm = 1728mm³ NB. Dimensions must be the same units! Volume = 25cm × 20cm × 150cm = 75000cm³ OR Volume = 0.25m × 0.2m × 1.5m = 0.075m³

What next? Print out the notes called PAV5a-Volume. Read through them and make sure you answer any questions. Work through the MyMaths lesson and its online homework called Volume of Cuboids found at: http://app.mymaths.co.uk/335-resource/volume-of-cuboids http://app.mymaths.co.uk/335-homework/volume-of-cuboids Save and complete the worksheet called Volume-S1.xlsx Now move on to the PAV5b powerpoint