Volume volume capacity cubic units rectangular prism estimation formulae triangular solid layers base cylinder cross-section circle uniform square units perpendicular solve

Cross-sections of prisms If all the slices through a solid have the same shape and size they have what we call a uniform cross-sectional area. The shaded face (or base, depending on your orientation) gives the name of the solid. A prism is a solid with a uniform cross-section.

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Drawing from a cross-section: Given each cross-section, draw the prism and name the solid that you have drawn.

Different views: Copy these prisms on isometric dot paper Construct the following shapes using centicubes and then draw a diagram of each one.

As we enter someone’s house we see the front view As we enter someone’s house we see the front view. If we look at the house from the neighbour’s view it would be the side view and if we approached the house from the rear it would be the back view. The architect’s floor plan of the house could be considered as the top view of the house (i.e. looking at the house from above). We could put all the views together to describe fully what the solid looks like. Draw the top, left side, right side and front views of this house.

Draw the top, the two sides and front views of this solid. Given the various views of a solid, draw a diagram of the solid on isometric paper.

Volume Volume refers to the amount of space that an object occupies. The volume of a solid is the number of cubic units that it occupies. The most common metric units for measuring volume are: cubic millimetres (mm 3 ) cubic centimetres (cm 3 ) cubic metres ( m 3 ). A cubic millimetre (1 mm 3 ) is the amount of space occupied by a cube of side length 1 mm.

Challenge! How many cubes? 73!

Formal Volume: Rather than count cubic units, we use a formula for the volume of a prism: V = (Area of cross-section) × h ( or V = A x h ) For a rectangular prism, this becomes: V = l × b × h or V = lbh where V = the volume, b = the breadth, l = the length and h = the height.

Composite Solids

Capacity The amount of liquid a container holds is referred to as its capacity. 1 L (1000 mL) = 1000 cm3 and 1 mL = 1 cm3

Larger Units for Capacity When dealing with larger volumes we use the following conversion: 1 m3 = 1000 L = 1 kL 1 kL means 1 kilolitre. This is equivalent to 1000 litres. A cube with sides length of 1 m would hold 1000 L or 1 kilolitre of liquid. 1 ML = 1 000 000 L = 1000 kL 5 6 7 8 9

Calculate the volume of the cylinder to the nearest cm3. Volumes of Cylinders The volume of a cylinder is found by: V = area of base (circle) × height V = Ah V = Calculate the volume of the cylinder to the nearest cm3.

Challenge Questions