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What is its volume when full? Find the capacity in litres when half full?

Mathematics

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2 parts
a

20400 cm3\text{}20400 \text{ cm}^3\text{}

b

10.2 litres\text{}10.2 \text{ litres}\text{}

Step-by-step solution

4 steps

Here is the solution for question 1 and 2:

The image shows a prism with a trapezoidal base. From the diagram, the top parallel side is 16 cm16 \text{ cm}, the height of the trapezoid is 17 cm17 \text{ cm}, and the length of the prism is 60 cm60 \text{ cm}. The bottom parallel side is marked as 'x'. By observing the grid, the top side is 8 grid units and the bottom side is 12 grid units. Since 16 cm16 \text{ cm} corresponds to 8 units, then 1 unit = 2 cm2 \text{ cm}. Thus, the bottom parallel side x=12×2 cm=24 cmx = 12 \times 2 \text{ cm} = 24 \text{ cm}.

Part a· 2 steps

What is its volume when full?

  1. Calculate the area of the trapezoidal base.

    The formula for the area of a trapezoid is A=12(a+b)hA = \frac{1}{2}(a+b)h, where aa and bb are the lengths of the parallel sides and hh is the perpendicular height.
    Here, a=16 cma = 16 \text{ cm}, b=24 cmb = 24 \text{ cm}, and h=17 cmh = 17 \text{ cm}.

    Abase=12(16 cm+24 cm)(17 cm)A_{base} = \frac{1}{2}(16 \text{ cm} + 24 \text{ cm})(17 \text{ cm}) Abase=12(40 cm)(17 cm)A_{base} = \frac{1}{2}(40 \text{ cm})(17 \text{ cm}) Abase=20 cm×17 cmA_{base} = 20 \text{ cm} \times 17 \text{ cm} Abase=340 cm2A_{base} = 340 \text{ cm}^2
  2. Calculate the volume of the prism when full.

    The formula for the volume of a prism is V=Abase×LengthV = A_{base} \times \text{Length}.
    Here, Abase=340 cm2A_{base} = 340 \text{ cm}^2 and Length =60 cm= 60 \text{ cm}.

    Vfull=340 cm2×60 cmV_{full} = 340 \text{ cm}^2 \times 60 \text{ cm} Vfull=20400 cm3V_{full} = 20400 \text{ cm}^3

    The volume when full is 20400 cm3\boxed{\text{}20400 \text{ cm}^3\text{}}

Part b

10.2 litres\text{}10.2 \text{ litres}\text{}

Find the capacity in litres when half full.

  1. Calculate the volume when the prism is half full.

    Vhalf=12×VfullV_{half} = \frac{1}{2} \times V_{full} Vhalf=12×20400 cm3V_{half} = \frac{1}{2} \times 20400 \text{ cm}^3 Vhalf=10200 cm3V_{half} = 10200 \text{ cm}^3
  2. Convert the volume from cubic centimetres to litres.

    We know that 1 litre=1000 cm31 \text{ litre} = 1000 \text{ cm}^3.

    Capacity in litres=Vhalf1000 cm3/litre\text{Capacity in litres} = \frac{V_{half}}{1000 \text{ cm}^3/\text{litre}} Capacity in litres=10200 cm31000 cm3/litre\text{Capacity in litres} = \frac{10200 \text{ cm}^3}{1000 \text{ cm}^3/\text{litre}} Capacity in litres=10.2 litres\text{Capacity in litres} = 10.2 \text{ litres}

    The capacity when half full is 10.2 litres\boxed{\text{}10.2 \text{ litres}\text{}}

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