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1.5 A basic geometrical shape with a circular base. 1.2.1 What kind of three-dimensional shape does the tank represent?

Mathematics

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Answer

r=1.2 Mr = \text{1.2 M}

C=7.536 MC = \text{7.536 M}

V=37.68 m3V = \text{37.68 m}^3

Step-by-step solution

6 steps

Here is the solution to Question 1:

1.1 Matching

  • 1.1.1 A basic shape with three angles and three sides. →\rightarrow D Triangle
  • 1.1.2 A line segment from the centre of the circle to the circle boundary. →\rightarrow F Radius
  • 1.1.3 A device that measures temperature. →\rightarrow A Thermometer
  • 1.1.4 The distance around the 2-dimensional shape. →\rightarrow B Perimeter
  • 1.1.5 A basic geometrical shape with a circular base. →\rightarrow C Cylinder

1.2 Water Tank Calculations

  • 1.2.1 What kind of three-dimensional shape does the tank represent? The tank represents a Cylinder.

  • 1.2.2 Calculate the radius of the water tank.

  1. Identify the given diameter.

    The diameter $D = 2.4 \text{ M}$.
    
  2. Calculate the radius using the formula r=D2r = \frac{D}{2}.

    $$
    r = \frac{2.4 \text{ M}}{2}
    $$
    $$
    r = \boxed{\text{1.2 M}}
    $$
    
    • 1.2.3 Calculate the circumference of the tank.
  3. Use the radius calculated in 1.2.2 and the given value for π\pi.

    Given $r = 1.2 \text{ M}$ and $\pi = 3.14$.
    
  4. Apply the formula for circumference C=2πrC = 2\pi r.

    $$
    C = 2 \times 3.14 \times 1.2 \text{ M}
    $$
    $$
    C = 6.28 \times 1.2 \text{ M}
    $$
    $$
    C = \boxed{\text{7.536 M}}
    $$
    
    • 1.2.4 Calculate the volume of water in m3^3 that the tank can hold if the radius of the dam is 2m and the height is 300cm.
  5. Identify the given dimensions and convert units if necessary.

    Given radius $r = 2 \text{ m}$.  
    Given height $h = 300 \text{ cm}$. Convert height to meters:
    $$
    h = 300 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 3 \text{ m}
    $$
    Use $\pi = 3.14$.
    
  6. Apply the formula for the volume of a cylinder V=πr2hV = \pi r^2 h.

    $$
    V = 3.14 \times (2 \text{ m})^2 \times 3 \text{ m}
    $$
    $$
    V = 3.14 \times 4 \text{ m}^2 \times 3 \text{ m}
    $$
    $$
    V = 3.14 \times 12 \text{ m}^3
    $$
    $$
    V = \boxed{\text{37.68 m}^3}
    $$
    
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