Term 2 Week 9

The final week of Perimeter Area and Volume

This week we consolidate this topic and will have an end of topic test Wednesday of week 10.

Volume. We will get our heads around the idea that we can calculate the volume of any prism by multiplying the area of the base times the vertical height.

So if we had a triangular prism (looking at the end you see a triangle) all we have to do is multiply the area of that triangle (1/2 base x height) by the length of the prism.

This is true for any prism - ie any shape that is 'extruded' like pasta. It does not matter how tricky the end looks if we can calculate the area of it then we can work out the volume of the whole shape.

The Perimeter, Area and Volume Assignment 3 is here

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Term 2 Week 8

This image is computer generated - which required the calculation of many thousands of areas of colour to render - the computer uses the same rules for area that we learn.

This week we move from calculating Perimeter to calculating area of shapes, and the the surface area of 3d shapes.

The secret is to know how to calculate the area of the standard shapes:

• Squares, rectangles, Parallelograms and Rhombus all have Area = base x vertical height

• Triangles have Area = 1/2 base x vertical height

• Kites and Rhombus have Area = 1/2 diagonal1 x diagonal2 (rhombus area can be calculated either way)

• Circles have Area = Pi x r², Part circles (sector) have Area = angle of sector / 360 x Pi x r²

The area of any shape that is a combination of the above shapes can be calculated by adding up (or subtracting as required) the area of the simpler shapes within it.

Calculating the surface are of 3d shapes is the same - just work out each basic shape and add up the areas. The only trick is to be sure that all of the sides of the object are included.

Perimeter, Area and Volume Assignment 2 is here

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Term 2 Week 7

The volume of Jupiter is more than that of all the other planets combined, but still only a small fraction of the volume of the sun.

This week we start the topic: Perimeter, Area and Volume. Students will already know how to work out the perimeter and volume of many shapes. This year we will extend that knowledge so students will be able to be able to add shapes or volumes together to make more complex shapes or volumes.

We will revisit Pythagoras so that lengths of right angle triangles can be computed. We will also do some calculations with circles and parts of circles (like pizza slices)

An example problem would be to work out the perimeter of a 20cm radius pizza slice - like you were an adventurous ant doing a walk around the edge of one. The pizza is divided equally into six parts.

To answer the question we need to add up the lines around the edge of the slice - there are two straight lines and a curved line. The straight ones are easy - they are just the radius of the circle - 2 x 20cm, but the round part is a little harder. We can find it by finding a fraction of the whole circle. - in this case 1/6th of a circle. So we multiply the circumference of the whole circle (Pi x diameter) by the fraction of a circle (1/6) . This gives us 3.14 x 40cm x 1/6 = 125.6/6 cm = ~ 31 cm. So the total edge of the slice is: 2 x 20 cm + 31 cm = 71 cm.

The Perimeter, Area and Volume assignment is here

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