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800 jerrycans fill a tank. One jerrycan weighs 20 kg. How many litres does the tank hold? A bucket contains 45.6 litres of water. The empty bucket weighs 3 kg. (i) What is the mass of the full bucket?

Mathematics

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Answers

2 parts
i

48.6 kg48.6 \text{ kg}

ii

45600 cm345600 \text{ cm}^3

Step-by-step solution

3 steps

Here are the solutions for problems 2 and 3.

:
"800 jerrycans fill a tank. One jerrycan weighs 20 kg. How many litres does the tank hold?"

Assumption: We assume that "One jerrycan weighs 20 kg" refers to the mass of the water contained in one jerrycan. We also use the density of water, where 1 kg of water has a volume of 1 litre.

Step 1: Determine the volume of water in one jerrycan.
Given that 1 kg of water is approximately 1 litre, if one jerrycan contains 20 kg of water, then its volume is 20 litres.

Volume per jerrycan=20 kg×1 L1 kg=20 L\text{Volume per jerrycan} = 20 \text{ kg} \times \frac{1 \text{ L}}{1 \text{ kg}} = 20 \text{ L}

Step 2: Calculate the total volume the tank holds.
The tank is filled by 800 jerrycans.

Total volume=Number of jerrycans×Volume per jerrycan\text{Total volume} = \text{Number of jerrycans} \times \text{Volume per jerrycan} Total volume=800×20 L\text{Total volume} = 800 \times 20 \text{ L} Total volume=16000 L\text{Total volume} = 16000 \text{ L}

The tank holds 16000 litres\boxed{16000 \text{ litres}}.

:
"A bucket contains 45.6 litres of water. The empty bucket weighs 3 kg."
"(i) What is the mass of the full bucket?"
"(ii) What is the volume of the water that fills the bucket in cm³?"

Part i· 2 steps

Mass of the full bucket

  1. Calculate the mass of the water.

    We use the density of water, where 1 litre of water has a mass of 1 kg.

    Mass of water=45.6 L×1 kg1 L=45.6 kg\text{Mass of water} = 45.6 \text{ L} \times \frac{1 \text{ kg}}{1 \text{ L}} = 45.6 \text{ kg}
  2. Calculate the total mass of the full bucket.

    Mass of full bucket=Mass of empty bucket+Mass of water\text{Mass of full bucket} = \text{Mass of empty bucket} + \text{Mass of water} Mass of full bucket=3 kg+45.6 kg\text{Mass of full bucket} = 3 \text{ kg} + 45.6 \text{ kg} Mass of full bucket=48.6 kg\text{Mass of full bucket} = 48.6 \text{ kg}

    The mass of the full bucket is 48.6 kg\boxed{48.6 \text{ kg}}.

Part ii

45600 cm345600 \text{ cm}^3

Volume of the water that fills the bucket in cm³

  1. Convert the volume from litres to cubic centimetres.

    We know that 1 litre is equal to 1000 cubic centimetres (1 L=1000 cm31 \text{ L} = 1000 \text{ cm}^3).

    Volume in cm3=45.6 L×1000 cm31 L\text{Volume in cm}^3 = 45.6 \text{ L} \times \frac{1000 \text{ cm}^3}{1 \text{ L}} Volume in cm3=45600 cm3\text{Volume in cm}^3 = 45600 \text{ cm}^3

    The volume of the water that fills the bucket is 45600 cm3\boxed{45600 \text{ cm}^3}.

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