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Volume, SM-Bank 012

Tennis balls are packaged in cylindrical containers.

Frank purchases a container of tennis balls that holds three standard tennis balls, stacked one on top of the other.

This container has a radius of 3.4 cm and a height of 20.4 cm, as shown in the diagram below.
 

  1. Calculate the volume of the cylinder in cubic centimetres, correct to one decimal place.  (2 marks)


  2. If one tennis ball has a volume of 164.6 cm³, how much unused volume, in cubic centimetres, surrounds the tennis balls in this container?
    Round your answer to the nearest whole number.  (1 mark)

Show Answers Only

a.    \(740.9\ \text{cm}^3\ \text{(to 1 d.p.)}\)

b.    \(247\ \text{cm}^3\ \text{(nearest cm}^3 \text{)}\)

Show Worked Solution
a.    
\(\text{Volume}\) \(=Ah\)
    \(=\pi\times 3.4^2\times 20.4\)
    \(= 740.86\dots\)
    \(=740.9\ \text{cm}^3\ \text{(to 1 d.p.)}\)

 

b.   
\(\text{Unused volume}\) \(=\text{cylinder volume}-\text{volume of balls}\)
    \(= 740.9-3\times 164.6\)
    \(= 247.1\)
    \(=247\ \text{cm}^3\ \text{(nearest cm}^3 text{)}\)