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Volume, SM-Bank 164

A half-cylinder has a height of 44 millimetres and a diameter of 20 millimetres. Calculate the volume of the half-cylinder in cubic centimetres, giving your answer as an exact value in terms of \(\pi\).  (2 marks)

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\(2200\pi\ \text{cm}^3\)

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\(\text{NOTE: change measurements to centimetres before calculations}\)

\(V\) \(=\dfrac{1}{2}\pi r^2h\)
  \(=\dfrac{1}{2}\times\pi\times 10^2\times 44\)
  \(=2200\pi\)

 
\(\therefore\ \text{The exact volume of the half-cylinder is }2200\pi\ \text{cm}^3\)

Volume, SM-Bank 163

A quarter-cylinder has a height of 160 centimetres and a radius of 800 centimetres . Calculate the volume of the quarter-cylinder in cubic metres, giving your answer as an exact value in terms of \(\pi\).  (2 marks)

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\(25.6\pi\ \text{m}^3\)

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\(\text{NOTE: change measurements to metres before calculations}\)

\(V\) \(=\dfrac{1}{4}\pi r^2h\)
  \(=\dfrac{1}{4}\times\pi\times 8^2\times 1.6\)
  \(=25.6\pi\)

 
\(\therefore\ \text{The exact volume of the quarter-cylinder is }25.6\pi\ \text{m}^3\)

Volume, SM-Bank 162

A half-cylinder has a height of 12 centimetres and a radius of 9 centimetres. Calculate the volume of the half-cylinder, giving your answer as an exact value in terms of \(\pi\).  (2 marks)

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\(486\pi\ \text{cm}^3\)

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\(V\) \(=\dfrac{1}{2}\pi r^2h\)
  \(=\dfrac{1}{2}\times\pi\times 9^2\times 12\)
  \(=486\pi\)

 
\(\therefore\ \text{The exact volume of the half-cylinder is }486\pi\ \text{cm}^3\)

Volume, SM-Bank 146

Geraldine created a large chocolate mould in the shape of a half cylinder using her 3D printer.
 

  1. Calculate the volume of the mould, giving your answer to the nearest cubic centimetre.  (2 marks)
  2. Calculate the capacity of the mould in litres.  (1 mark)
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a.    \(8310\ \text{cm}^3\)

b.    \(8.31\ \text{L}\)

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a.    \(\text{diameter = 23 cm }\rightarrow\ \text{radius = 11.5 cm}\)

\(\therefore\ V\) \(=\dfrac{1}{2}\times \pi r^2h\)
  \(=\dfrac{1}{2}\times \pi\times 11.5^2\times 41\)
  \(=8309.512\dots\)
  \(\approx 8310\ \text{cm}^3\ \text{nearest cm}^3)\)

 

b.    \(\text{1 litre = 1000 cm}^3\)

\(\therefore\ 8310\ \text{cm}^3\) \(=\Bigg(\dfrac{8310}{1000}\Bigg)\ \text{L}\)
  \(=8.31\ \text{L}\)

Volume, SM-Bank 145

Calculate the volume of the figure below in cubic millimetres. Give your answer correct to 1 decimal place.  (2 marks)
 

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\(942.5\ \text{mm}^3\)

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\(\text{Figure is }\dfrac{60}{360}=\dfrac{1}{6}\ \text{of a cylinder}\)

\(\therefore\ V\) \(=\dfrac{1}{6}\times \pi r^2h\)
  \(=\dfrac{1}{6}\times \pi\times 10^2\times 18\)
  \(=942.477\dots\)
  \(\approx 942.5\ \text{mm}^3\ (\text{1 d.p.})\)

Volume, SM-Bank 144

Calculate the volume of the figure below in cubic metres. Give your answer correct to 1 decimal place.  (2 marks)
 

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\(17.9\ \text{m}^3\)

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\(\text{Figure is }\dfrac{3}{4}\ \text{of a cylinder}\)

\(\therefore\ V\) \(=\dfrac{3}{4}\times \pi r^2h\)
  \(=\dfrac{3}{4}\times \pi\times 1.3^2\times 4.5\)
  \(=17.918\dots\)
  \(\approx 17.9\ \text{m}^3\ (\text{1 d.p.})\)

Volume, SM-Bank 143

Calculate the volume of the quarter cylinder below in cubic centimetres.  Give your answer correct to the nearest cubic centimetre.  (2 marks)
 

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\(113\ \text{cm}^3\)

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\(V\) \(=\dfrac{1}{4}\times \pi r^2h\)
  \(=\dfrac{1}{4}\times \pi\times 4^2\times 9\)
  \(=113.097\dots\)
  \(\approx 113\ \text{cm}^3\ (\text{nearest cubic cm.})\)

Volume, SM-Bank 006

A tent with semicircular ends is in the shape of a prism. The diameter of the ends is 1.5 m. The tent is 2.5 m long.
 

GEOMETRY, FUR1 2008 VCAA 6 MC

Calculate the total volume of the tent in cubic metres, correct to one decimal place.  (2 marks)

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\(2.2\ \text{m}^3\ \text{(1 d.p.)}\)

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\(\text{Diameter}=1.5\ \text{metres}\ \ \Rightarrow\ \ \ \text{Radius}= \dfrac{1.5}{2} = 0.75\ \text{metres}\)

\(V\) \(=\dfrac{1}{2}\times \pi r^2h\)
  \(=\dfrac{1}{2}\times \pi\times 0.75^2\times 2.5\)
  \(=2.2089\dots\)
  \(\approx 2.2\ \text{m}^3\ \text{(1 d.p.)}\)