Try some yourself
Question 1
Find the volumes of these objects.
Answer
(a)
So
volume = 50.265 cm^{2} × 10 cm = 502.65 cm^{3}.
Thus the volume is 503 cm^{3} (to the nearest cubic centimetre).
(If you used the approximate value of 3.14 for , you will have got a crosssectional area of 50.24 cm^{2} and a volume of 502.4 cm^{3}.)

(b)
So
volume = 37.5 m^{2} × 10 m = 375 m^{3}.
Question 2
Two car manufacturers both claim that their models have an engine capacity of 2 litres. The two models have fourcylinder, fourstroke engines.
The table below shows the details of the four cylinders.
Car model  Cylinder diameter (bore)/mm  Cylinder height (stroke)/mm  Number of cylinders 

A  86  86  4 
B  92  75  4 
By working out the total volume of the four cylinders for each model in cm^{3}, find out if the manufacturers’ claims are true.
(Hint: 1 litre = 1000 cm^{3}.)
Answer
Car A has four cylinders, each with a radius of 4.3 cm and a height of 8.6 cm. The volume of one cylinder is calculated by using the formula
So, the four cylinders will have
Car B has four cylinders, each with a radius of 4.6 cm and a height of 7.5 cm. From the same formula, the four cylinders will have
Therefore, both engines have a cubic capacity very close to 2000 cm^{3}. They are both said to have twolitre engines. Hence the claims of both manufacturers are true.
Question 3
The guttering pictured here has a semicircular crosssection. Find the volume of water that the guttering will hold when full.
Answer
The crosssection of the guttering is a semicircle of radius 0.05 m. So
Then, since the length of the guttering is 12m,
Therefore the guttering will hold about 0.047 m^{3} of water.