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Volume, SM-Bank 079 MC

A sculpture is pictured from 3 different angles below:
 

 
The sculpture is in the shape of

  1. a trapezium and a circle.
  2. a trapezium and a cylinder.
  3. a sphere and a prism.
  4. a cylinder and a prism.
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\(D\)

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\(\text{The bottom shape is a trapezoidal prism (not a trapezium).}\)

\(\therefore\ \text{The sculpture is in the shape of a cylinder and a prism.}\)

\(\Rightarrow D\)

Volume, SM-Bank 067

A triangular prism has a volume of 680 cubic centimetres and a height of 5 centimetres. What is the cross-sectional area?  (2 marks)

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\(136\ \text{m}^2\)

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\(V\) \(=Ah\)
\(680\) \(=A\times 5\)
\(A\) \(=\dfrac{680}{5}\)
  \(=136\)

 
\(\therefore\ \text{The cross-sectional area is }136\ \text{m}^2.\)

Volume, SM-Bank 054

The prism below has a height of 100 metres.

Given its volume is 485 cubic metres, calculate the cross-sectional area, \((A)\), of the prism.  (2 marks)
 

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\(4.85\ \text{m}^2\)

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\(V=485\ \text{m}^3\ \text{and }h=100\ \text{m}\)

\(V\) \(=Ah\)
\(485\) \(=100A\)
\(A\) \(=\dfrac{485}{100}\)
\(A\) \(=4.85\ \text{m}^2\)

Volume, SM-Bank 053

The prism below has a height of 23 centimetres.

Given its volume is 391 cubic centimetres, calculate the cross-sectional area, \((A)\), of the prism.  (2 marks)
 

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\(17\ \text{cm}^2\)

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\(V=391\ \text{cm}^3\ \text{and }h=23\ \text{cm}\)

\(V\) \(=Ah\)
\(391\) \(=23A\)
\(A\) \(=\dfrac{391}{23}\)
\(A\) \(=17\ \text{cm}^2\)

Volume, SM-Bank 052

The prism below has a cross-sectional area of 15 square millimetres.

Given its volume is 184.5 cubic millimetres, calculate the height, \((h)\), of the prism.  (2 marks)
 

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\(12.3\ \text{mm}\)

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\(V=184.5\ \text{mm}^3\ \text{and }A=15\ \text{mm}^2\)

\(V\) \(=Ah\)
\(184.5\) \(=15h\)
\(h\) \(=\dfrac{184.5}{15}\)
\(h\) \(=12.3\ \text{mm}\)

Volume, SM-Bank 051

The prism below has a cross-sectional area of 50 square centimetres.

Its volume is 425 cubic centimetres.
 

Calculate the height, \((h)\), of the prism.  (2 marks)

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\(8.5\ \text{cm}\)

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\(V=425\ \text{cm}^3\ \text{and }A=50\ \text{cm}^2\)

\(V\) \(=Ah\)
\(425\) \(=50h\)
\(h\) \(=\dfrac{425}{50}\)
\(h\) \(=8.5\ \text{cm}\)

Volume, SM-Bank 016

A concrete staircase leading up to the grandstand has 10 steps.

The staircase is 1.6 m high and 3.0 m deep.

Its cross-section comprises identical rectangles.

One of these rectangles is shaded in the diagram below.

  1. Find the area of the shaded rectangle in square metres.  (2 marks)


The concrete staircase is 2.5 m wide.

  1. Find the volume of the solid concrete staircase in cubic metres.  (2 marks)

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a.    \(0.048\ \text{m}^2\)

b.    \(6.6\ \text{m}^3\)

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a.   \(\text{Height of rectangle}\)

\(=\dfrac{1.6}{10}\)

\(=0.16\ \text{m}\)

\(\text{Length of rectangle}\)

\(=\dfrac{3.0}{10}\)

\(= 0.3\ \text{m}\)

\(\therefore\ \text{Area of rectangle}\) \(=0.16\times 0.3\)
  \(=0.048\ \text{m}^2\)

 

b.    \(\text{55 rectangles make up the cross-section}:\)

\(\therefore\ A\) \(=55\times 0.048\)
  \(= 2.64\ \text{m}^2\)

 

\(\therefore\ V\) \(=Ah\)
  \(=2.64\times 2.5\)
  \(=6.6\ \text{m}^3\)

Volume, SM-Bank 015

Khaleda manufactures a face cream. The cream comes in a cylindrical container.

The area of the circular base is 43 cm2. The container has a height of 7 cm, as shown in the diagram below.
 

What is the volume of the container in cubic centimetre?   (2 marks)

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\(301\ \text{cm}^3\)

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\(V\) \(=\text{Area of base}\times \text{height}\)
  \(=43\times 7\)
  \(=301\ \text{cm}^3\)

Volume, SM-Bank 003 MC

A steel beam used for constructing a building has a cross-sectional area of 0.048 m2 as shown.

The beam is 12 m long.
 


 

In cubic metres, the volume of this steel beam is closest to

  1. \(0.576\)
  2. \(2.5\)
  3. \(2.63\)
  4. \(57.6\)
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\(A\)

Show Worked Solution
\(\text{Volume}\) \(=A\times h\)
  \(=0.048\times 12\)
  \(=0.576\ \text{m}^3\)

 
\(\Rightarrow A\)