Perimeter Area and Volume

The 1st question in the chapter test is a perfect example of an exam type question, so you should take about 25 minutes to answer it.
For part a)
Use the area of a circle formula (area = πr²) twice for the larger circle and for the smaller one, making sure to do as you're told with π = 22/7.
Do not fall into the trap of thinking you can subtract the radii and find the area of a circle with radius = 7cm. If in doubt, sketch out the circles.

For part b)
You need to use the formulae for volume of a sphere and volume of a cylinder.
Part iii of this question is a little confusing. They are looking for the volume of air that is left in the cylinder when it contains the 3 balls.

Fort part c)
This is a tricky question. You are told the radius of the hemisphere so first step is to work out its volume. Note that the question doesn't mention whether π should be 3.14 or 22/7. That is because you can actually work out the answer conveniently without setting π equal to anything, just leave your work in terms of π.
When you find the volume of the hemisphere, you know that the volume of a cone is half of this.
So work out half the volume of the hemisphere (in terms of π) and then set up an equation with the formula for volume of a cone on the left (subbing r = 6) and the volume you just calculated on the right.
An example (not accurate for this question). Lets say the volume of the hemisphere turns out to be 20π. Then write down
1/3π r²h = 10π and sub in the value of the radius on the left.
To simplify your equation, first divide across by π (gets rid of both πs) and multiply across by 3 (gets rid of the fraction). Then solve for h, the only unknown.
Don't lose sight of what you were originally asked. The height of the entire shape is equal to this height plus the radius of the hemisphere. Make sure you can understand why.

General point:
If you are working out e.g. πr² make sure that you understand fully that it is only r which gets squared and that the result of r² gets multiplied by π.
You never square or cube π.