Chapter 9 Solid Geometry

Module PMR

CHAPTER 9 : SOLID GEOMETRY

1. Geometric solids are three – dimensional shapes that have length, breadth and height. 2. Examples of geometric solids include cubes, cuboids, cylinders, pyramids, cones and spheres. 3. The layout or the net of a geometric is a two – dimensional shapes that is obtained by opening up the geometric solid. For example,

a) Cube b) Cuboid

c) Prism

d) Pyramid

e) Cylinder

f) Cone

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3. Volume is the measurement of a three – dimensional space. i.

Volume of a cube = length x breadth x height (length=breadth=height) Find the volume of the following cubes

Example :

Exercise : 1.

1 cm

3 cm

Volume = 3 × 3 × 3 = 27 cm2

Volume =

2.

3.

2 mm 4 cm

Volume =

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Volume =

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ii. Volume of a cuboid = length x breadth x height Find the volume of the following cuboids

Example :

Exercise : 1. 4 cm 11 cm

5 cm 6 cm

3 cm 10 cm

Volume = 6 × 5 × 4 = 120 cm2

Volume =

2.

3.

9 mm

0.2 m 1m

4 cm

1.5 m 9 mm

Volume =

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Volume =

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4. Solving problems. Example :

5 cm The figure above shows a cuboid. Given that the volume of the cuboid is 250 cm3, find the height of the cuboid.

Volume = length x breadth x height 250 = 5 × 5 × height 250 Height = 25 = 10 cm. ∴ The height of the cuboid is 10 cm.

1. 5 cm

8 cm The figure above shows a cuboid of volume 240 cm3. Find the breadth of the cuboid.

2. 8m 8m ℓm The figure above shows a container of volume 512 m3. Find the value of ℓ .

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3. A box is in the form of a cuboid 40 cm long, 30 cm wide and 25 cm high. How many cubes, of edge 5 cm each can be packed into the box?

4.

2m The figure above shows the layout of a cube which is made of metal. If the cube is formed, find its volume.

5. 6 cm 3 cm ℓ cm

The volume of the cuboid above is equivalent to the total volume of 6 cubes each of sides 3 cm. Find the value of ℓ .

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PMR past year questions 1. The question is on drawing a full scale the net of a given geometric solid. 2. Tips: a. Use pencil and ruler to draw. b. Draft the drawing before transferring the drawing on the square grids. c. Clean drawing. d. Do not label unless it is required by the question. 3. Mistakes students often made a. Sketch the net. b. Unclean drawing. c. Double lines. d. Incorrect size of the net e. The vertices are not joined, not a closed figure. Exercise State the types of solids that have the following layouts.

1.

4.

2.

5.

3. 6.

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Example 1 : 1 cm 2cm 3cm The diagram above shows a cuboid. Draw a net of the cuboid on the grid of squares below.

Exercise 1 :

1 cm 3cm 4cm The diagram above shows a cuboid. Draw a net of the cuboid on the grid of squares below.

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Example 2 : Complete the net of a cube below.

Exercise 2 :

Complete the net of a cube below.

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PMR past year questions 2004. 1. Diagram below shows a right pyramid with a square base.

5 units

6 units

Draw a full scale the net of the pyramid on the grid in the answer space. The grid has equal squares with sides of 1 unit. Answer :

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2007 2. Diagram below shows a prism. One of the surfaces of the net of the prism is drawn on a square grid with sides of 1 unit in the answer space.

4 units

7 units 3 units Complete the net of the prism.

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CHAPTER 7 : SOLID GEOMETRY ANSWERS 3. i. Volume of a cube

4. Solving problems 1. 6 cm 2. 8 3. 240 cubes 4. 0.125 m3 5. 9

1. 1 cm3 2. 64 cm3 3. 8 mm3

EXERCISE ii. Volume of a cuboid

1. Prism 2. Pyramid 3.Cube 4. Cuboid 5. Cylinder 6. Cone

1. 330 cm3 2. 0.3 m3 d. 3 240 mm3

2.

3.

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PMR 2004

PMR 2007

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