Perimeter Area and Volume

For my one-page overview you can look at the previous entry.

In class on Thursday, we looked at the different types of questions you can get asked for perimeter, area and volume.

Finding area and perimeter of rectangular shapes and triangles
Irregular rectangular shapes: break them into smaller rectangles.
Triangles: half the base by the perpendicular height.
[Area of a triangle of where base = 8cm and perpendicular height = 3cm multiply as follows
1/2 x 8 x 3 = 12cm²]

Volume of a prism (any rectangular solid with a uniform cross-section)
Find the area of the uniform cross-section and multiply this by the length of the prism.

Circular shapes
The first question is how to handle π, pi.
The most important thing is to follow instructions, using 22/7, 3.14 or giving your answer in terms of π.
Know where to find the formulae you need.

Trickier questions
Changing shapes
If a solid in one shape is being melted down and recast into another shape you need to set up an equation. If both shapes are circular (eg a sphere being melted down into a cylinder, or liquid in a cylindrical jug being poured into smaller cylindrical tumblers) then the πs on both sides of the equation will cancel. In questions like this you will not be told how to handle π.
Liquid in a pipe
Water flows in a pipe at the rate if 50cm/sec. The pipe has a radius of 2cm. How long will it take to fill a tank measuring 30cm x 30cm x 100cm.
To answer a question like this, consider a single molecule of H2O in the pipe. It takes 1 second to travel 50cm - that means that in the space of 1 second all the molecules are replaced. If you find the volume of 50cm of pipe you will have 1 second's worth of water.
[This is π x 4² x 50]
Then find the volume of the tank
[This is 30 x 30 x 50]
Finally divide the first answer into the second answer to find the time in seconds.
Then convert to minutes or hours as required.