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Measurement, STD2 EQ-Bank 13 MC

A square pyramid has a base with side length 9 cm and a perpendicular height of 8 cm.

Calculate the volume of the pyramid. 

  1. 72 cm³
  2. 144 cm³
  3. 192 cm³
  4. 216 cm³
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\(D\)

Show Worked Solution

\(A=9^2=81\)

\(V\) \(=\frac{1}{3}Ah\)
  \(=\frac{1}{3}\times 81\times 8\)
  \(=216\ \text{cm}^3\)

  
\(\Rightarrow D\)

Measurement, STD2 EQ-Bank 4 MC

A cone has a radius of 6 cm and a height of 8 cm.

Calculate the volume of the cone, giving your answer in cubic centimetres correct to 1 decimal place.

  1. 100.5 cm³
  2. 150.8 cm³
  3. 301.6 cm³
  4. 904.8 cm³
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\(C\)

Show Worked Solution
\(V\) \(=\frac{1}{3}\pi r^2h\)
  \(=\frac{1}{3}\times \pi \times (6)^2\times 8\)
  \(=301.592\dots\)
  \(=301.6\ \text{cm}^3 \text{(1 d.p.)}\)

  
\(\Rightarrow C\)

Measurement, STD2 EQ-Bank 19

The cone below has a diameter of 13.5 centimetres and a height of 0.4 metres.
 

Calculate the volume of the cone, giving your answer in cubic centimetres correct to 1 decimal place.   (2 marks)

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\(1908.5\ \text{cm}^3 \text{(1 d.p.)}\)

Show Worked Solution

\(\text{Radius}\ =\dfrac{13.5}{2}=6.75\ \text{cm}\)

\(0.4\ \text{m}\ =\ 40\ \text{cm}\)

\(V\) \(=\frac{1}{3}\pi r^2h\)
  \(=\frac{1}{3}\times \pi \times (6.75)^2\times 40\)
  \(=1908.517\dots\)
  \(=1908.5\ \text{cm}^3 \text{(1 d.p.)}\)

Measurement, STD2 EQ-Bank 18

The cone below has a radius of 4.2 metres and a height of 6.1 metres.
 

Calculate the volume of the cone, giving your answer in cubic metres correct to 1 decimal point.   (2 marks)

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\(112.7\ \text{m}^3 \text{(1 d.p.)}\)

Show Worked Solution
\(V\) \(=\frac{1}{3}\pi r^2h\)
  \(=\frac{1}{3}\times \pi \times (4.2)^2\times 6.1\)
  \(=112.682\dots\)
  \(=112.7\ \text{m}^3 \text{(1 d.p.)}\)

Measurement, STD2 EQ-Bank 16

The square pyramid below, has a side measurement of 120 metres and a perpendicular height \((h)\) of 65 metres.
 

Find the volume of the pyramid in cubic metres.   (2 marks)

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\(312\, 000\ \text{m}^3\)

Show Worked Solution
\(V\) \(=\frac{1}{3}Ah\)
  \(=\frac{1}{3}\times 120\times 120\times 65\)
  \(=312\, 000\ \text{m}^3\)

Measurement, STD2 EQ-Bank 23

A cone with a radius 9.5 cm and height 19.5 cm is shown.
 

The cone is filled with liquid. 

Find the amount of liquid in the cone. Give your answer in litres correct to 3 decimal places.   (3 marks)

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\(1.843\ \text{L}\)

Show Worked Solution
\(V\) \(=\frac{1}{3}\pi r^2h\)
  \(=\frac{1}{3}\pi (9.5)^2\times 19.5\)
  \(=1842.93679\ \text{cm}^3\)

 
\(\text{Since 1 cm\(^3\) = 1 mL  and  1 L = 1000 mL:}\)

\(\text{Liquid in cone}=\dfrac{1842.9…}{1000}=1.8429…=1.843\ \text{litres (3 d.p.)}\)

Measurement, STD2 M1 2015 HSC 8 MC

The Louvre Pyramid in Paris has a square base with side length 35 m and a perpendicular height of 22 m.
 

What is the volume of this pyramid, to the nearest m³?

  1. `257\ text(m)^3`
  2. `1027\ text(m)^3`
  3. `8983\ text(m)^3`
  4. `26\ 950\ text(m)^3`
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`C`

Show Worked Solution
`V` `= 1/3Ah`
`A` `= 35 xx 35`
  `= 1225\ text(m)^2`

 

`:.V` `= 1/3 xx 1225 xx 22`
  `= 8983.33…\ text(m)^3`

 
`=>C`

Measurement, STD2 M1 2013 HSC 12 MC

A square pyramid fits exactly on top of a cube to form a solid.

2013 12 mc

What is the volume of the solid?

  1. 513 cm³
  2. 999 cm³
  3. 1242 cm³
  4. 1539 cm³
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`B`

Show Worked Solution
`text(Volume )` `=text{Vol (cube)} +text{Vol (pyramid)}`
  `=l^3+1/3Ah`
  `=(9xx9xx9)+(1/3xx9xx9xx10)`
  `=999\ text(cm)^3`

 
`=>\ B`