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Miriam is trying to find the volume of the water tank shown in the photograph on the right - Junior Cycle Mathematics - Question 13 - 2015

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Question 13

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Miriam is trying to find the volume of the water tank shown in the photograph on the right. She takes some measurements and draws a diagram. Part of her diagram is ... show full transcript

Worked Solution & Example Answer:Miriam is trying to find the volume of the water tank shown in the photograph on the right - Junior Cycle Mathematics - Question 13 - 2015

Step 1

Using the diagram, find the value of $x$. Give your answer in metres, correct to two decimal places.

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Answer

To find the value of xx, we can use the tangent function from trigonometry:

an(30ext°)=20x an(30^{ ext{°}}) = \frac{20}{x}

This gives us:

x=20tan⁡(30ext°)=2013=203x = \frac{20}{\tan(30^{ ext{°}})} = \frac{20}{\frac{1}{\sqrt{3}}} = 20\sqrt{3}

Calculating this: x≈11.55x \approx 11.55 m (to two decimal places).

Step 2

Find the distance marked $h$ on the photograph. Give your answer correct to one decimal place.

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Answer

To find hh, we first note the angles of elevation:

  1. For the bottom of the tank: 30°
  2. For the top of the tank: 38°

Using the first angle:

x+h=20tan⁡(38ext°)x + h = 20 \tan(38^{ ext{°}})

Substituting xx: h=20tan⁡(38ext°)−11.55h = 20 \tan(38^{ ext{°}}) - 11.55

Calculating this gives: h≈16.63−11.55≈5.08h \approx 16.63 - 11.55 \approx 5.08

So, h≈4.1h \approx 4.1 m (to one decimal place).

Step 3

State clearly what shape you are taking the water tank to be.

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Answer

The shape of the water tank is taken to be a Cylinder.

Step 4

Measurements from photograph (label each measurement):

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Answer

Diameter = 5.2 cm [Radius = 2.6 cm, Height = 2.2 cm]

Step 5

Calculations:

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Answer

To calculate the volume of the cylinder:

  • Actual radius: 4.52.2=5.318...m \frac{4.5}{2.2} = 5.318... m
  • Volume of cylinder: V=πr2h=π(5.318)2×4.5V = \pi r^2 h = \pi (5.318)^2 \times 4.5

Calculating: V≈399.81m3V \approx 399.81 m^3 Rounded to the nearest m³, the volume of the water tank is 400 m³.

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