SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, STD2 M1 2014 HSC 28d*

An aerial diagram of a swimming pool is shown. 

The swimming pool is a standard length of 50 metres but is not in the shape of a rectangle.

In the diagram of the swimming pool, the five widths are measured to be: 

`CD = 21.88\ text(m)`

`EF = 25.63\ text(m)`

`GH = 31.88\ text(m)`

`IJ = 36.25\ text(m)`

`KL = 21.88\ text(m)` 
 

  1. Use four applications of the Trapezoidal Rule to calculate the surface area of the pool.   (2 marks)

  2.  The average depth of the pool is 1.2 m

     

    Calculate the approximate volume of the swimming pool, in litres.   (1 mark)

Show Answers Only
  1. `1445.5\ text(m)^2`
  2. `1\ 734\ 600\ text(L)`
Show Worked Solution

a.    `\text{Strategy 1}`

`text(Surface Area of pool)`

`~~ 12.5/2(21.88 + 25.63) + 12.5/2(25.63+31.88)+12.5/2(31.88+36.25)  …`

`+ 12.5/2(36.25 + 21.88)`

`~~ 1445.5\ text(m)^2`
 

`\text{Strategy 2}`

`text(Surface Area of pool)`

`~~ 12.5/2[21.88 + 2(25.63 + 31.88 + 36.25) + 21.88]`

`~~ 1445.5\ text(m)^2`
 

♦ Mean mark (b) 50%.
b.    `V` `= Ah`
    `~~ 1445.5 xx 1.2`
    `~~ 1734.6\ text(m)^3`
    `~~ 1\ 734\ 600\ text(L)`

Measurement, STD2 M1 EQ-Bank 11 MC

The diagram represents a field.
 

What is the area of the field, using four applications of the Trapezoidal’s rule?

  1. 105 m²
  2. 136 m²
  3. 210 m²
  4. 420 m²
Show Answers Only

`A`

Show Worked Solution

`text(Solution 1)`

`text(Area)` `~~ 3/2(6 + 7) + 3/2(7 + 12) + 3/2(12 + 8) + 3/2(8 + 10)`
  `~~ 3/2(13 + 19 + 20 + 18)`
  `~~ 105\ text(m)^2`

 

`text(Solution 2)`

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & 0 & 3 & 6 & 9 & 12 \\
\hline
\rule{0pt}{2.5ex} \text{height} \rule[-1ex]{0pt}{0pt} & \ \ \ 6\ \ \  & \ \ \ 7\ \ \  & \ \ 12\ \  & \ \ \ 8\ \ \  & \ \ 10\ \  \\
\hline
\rule{0pt}{2.5ex} \text{weight} \rule[-1ex]{0pt}{0pt} & 1 & 2 & 2 & 2 & 1 \\
\hline
\end{array}

`text(Area)` `~~ 3/2(6 + 2 xx 7 + 2 xx 12 + 2 xx 8 + 10)`
  `~~ 3/2(70)`
  `~~ 105\ text(m)^2`

 
`=> A`

Measurement, STD2 M1 2018 HSC 28a

A field is bordered on one side by a straight road and on the other side by a river, as shown. Measurements are taken perpendicular to the road every 7.5 metres along the road.
 

Use four applications of the Trapeziodal rule to find an approximation to the area of the field. Answer to the nearest square metre.   (3 marks)

Show Answers Only

`242\ text{m}^2`

Show Worked Solution

`text(Strategy 1)`

`A` `~~ 7.5/2(8.8 + 7.1) + 7.5/2(7.1 + 9.8) + 7.5/2(9.8 + 8.5) + 7.5/2(8.5 + 4.9)`
  `~~ 241.875`
  `~~ 242\ text{m}^2\ \text{(nearest m}^2\text{)}`

 

`text(Strategy 2)`

`A` `~~ 7.5/2(8.8 + 2 xx 7.1 + 2 xx 9.8 + 2 xx 8.5 + 4.9)`
  `~~ 242\ text{m}^2\ \text{(nearest m}^2\text{)}`

Measurement, STD2 M1 EQ-Bank 21

A farmer wants to estimate the area of an irregular shaped paddock.
 

 
What is the estimated area of the land using the Trapezoidal Rule?   (2 marks)

Show Answers Only

`370\ text(m)^2`

Show Worked Solution

`text(Solution 1)`

`text(Height) = 20 div 4 = 5\ text(m)`

`text(Area)` `~~ 5/2 (28 + 18) + 5/2 (18 + 17) + 5/2 (17 + 16) + 5/2 (16 + 18)`
  `~~ 370\ text(m)^2`

 
`text(Solution 2)`

  `x` `0` `5` `10` `15` `20`
  `text(height)` `28` `18` `17` `16` `18`
  `text(weight)` `1` `2` `2` `2` `1`
`text(Area)` `~~ h/2 [28 + 2 (18 + 17 + 16) + 18]`
  `~~ 5/2 xx 148`
  `~~ 370\ text(m)^2`