# 2.2 Space and shape

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## Space and shape

Activity 1:

To understand the structure of some regular right prisms

[LO 3.3, 3.4]

A. Building cont a iners

You will be given a sheet of shapes. You will need a ruler that you can measure with, a pair of scissors and glue or sticky tape. Colouring pens will also be helpful. Do the following with these shapes:

1. Carefully measure all the lines and write down your measurements ( you should be able to measure to the nearest half–millimetre). You must also do your best to measure the radius (or diameter) of the circle. If you have a protractor available, find out where the 90°–angles are.
2. Using these measurements, calculate the areas of the different shapes, and add the parts together to find out the total area of each of the four shapes. Set your work out very clearly so that anybody can understand what you have done. Use the proper names for the shapes you describe.

For example, for the last figure you could say:

Total area = small rectangle + small rectangle + large rectangle

= ( l × b ) + ( l × b ) + ( l × b )

and so on . . . (Remember to use appropriate units.)

1. Very carefully cut out the given shapes. You can colour these shapes to make it easier to see which the top and base are, and which the sides (the sides are striped). Now fold them and use tape, or glue and paper strips, to make four boxes. Keep the sides with the dotted lines on the outside.
2. Write down what the Total Surface Area (TSA) of each shape is. (You have already calculated the answer!)
3. Work in groups of two or three to try to find out how many 1cm × 1cm blocks will fit into each box. This is called the volume of the box. If you can find a method or a formula that will work with each of the four shapes, write that down carefully.
4. At the end of this exercise, you should have two formulas.

B. Right prisms

• Each of the four boxes is a right prism . These are shapes with a top and base that are exactly the same size and shape, and sides that go up straight at right angles to the base. Look around to see whether you can discover shapes with these characteristics.
• We name right prisms according to the shape of the base, e.g. square prism, rectangular prism, triangular prism and circular prism (cylinder).
• Are these two shapes right prisms? Describe the shape of the base of each, and confirm whether the sides go straight up at right angles to the base.
• What kind of work did you do in this section? Score yourself in this table.
 Did i work Excellent Adequately Not well enough well with my team? according to instructions? carefully? accurately? neatly?

C. Formul a s

• To calculate the total surface area (TSA) and volume (V) of any right prism we use the following general formulas: (Please note that H refers to the prism height.)

TSA = 2 × base area + sides area and V = base area × prism height

Here are some important e x amples. These are the cut–out prisms you made into boxes. Please note how each part of the calculation is done separately and then put into the formula at the end.

1. Squ a re prism :

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