In this chapter, we are going to explore the concept of capacity and find out why it is important as well as its measurement. Using the concept of capacity, we can figure out how much space is available in a container. From the cups we use to drink to the water park we are playing in, it is all about capacity.
Capacity means how much liquid you can hold in your container. Consider it like the amount of water that a glass can contain.
Look at these four cans:
The first can hold 25 L, the second can hold 50 L, the third can hold 75 L and the fourth can hold 100 L. Therefore, it shows that different cans hold different amounts of liquid. Hence, the capacity is different for different cans.
Another term often used with capacity is volume. Volume signifies the amount of space contained within a closed container.
The primary units for measuring capacity or volume are litres (L) and millilitres (mL). The relationship between litres and millilitres is defined as follows:
1 litre (L) is equal to 1000 millilitres (mL)
This conversion factor allows for easy transitions between litres and millilitres when measuring the volume or capacity of liquids or substances.
Capacity is measured using measuring cups, measuring funnels, measuring beakers, measuring cylinders, etc.
Metric units and non-metric units are used to measure capacity or volume.
In the metric system, capacity is measured in units such as litres (L), millilitres (mL) and centilitres. When a numerical value is followed by "L" or "mL", it indicates the quantity the container can hold without spilling over.
Conversely, non-metric units of capacity include gallons, quarts, pints and others. These units are commonly employed in different regions to measure the volume of liquids or gases.
The figure shows metric units and non-metric units of capacity.
Conversion of Metric Units
To convert between different units of capacity, you can follow a simple rule:
a. When converting from a smaller unit of capacity to a larger unit, multiply the value associated with the smaller unit by 10.
b. When converting from a larger unit of capacity to a smaller unit, divide the value associated with the larger unit by 10.
This conversion process can be represented as follows:
The fundamental metric conversions for capacity are as follows:
Litres (L) to millilitres (mL):
→ 1 L = 1000 mL
→ To convert from litres to millilitres, you can multiply the number of litres by 1000.
→ Example: 3.5 L × 1000 mL = 3500 mL
Millilitres (mL) to Litres (L):
→ 1 mL = 1/1000 L = 0.001 L
→ To convert from millilitres to litres, you should divide the number of millilitres by 1000 or multiply the number of millilitres by 0.001.
→ Example: 500 mL ÷ 1000 = 0.5 L
Or
500 mL × 0.001 mL = 500 mL × (1/1000) = 0.5 L
If you measure the capacities or volumes, then these conversion rules can be used.
Conversion of Non-Metric Units
Here are the conversions for non-metric units commonly used to measure capacity:
Gallons to Quarts:
→ 1 Gallon = 4 Quarts
→ To convert from gallons to quarts, you should multiply the number of gallons by 4.
→ Example: 1.5 Gallons × 4 = 6 Quarts
Gallons to Pints:
→ 1 Gallon = 8 Pints.
→ To convert from gallons to pints, you should multiply the number of gallons by 8.
→ Example: 1.5 Gallons × 8 = 12 Pints
Quarts to Pints:
→ 1 Quart = 2 Pints
→ To convert from quarts to pints, you should multiply the number of quarts by 2.
→ Example: 1.5 Quarts × 2 = 3 Pints
These conversions provide a way to relate gallons, quarts and pints when measuring capacity in non-metric units.
Example 1: How many packets of milk with a capacity of 350 millilitres can be packed from 24.5 kilolitres of milk?
a) 3500
b) 35000
c) 7000
d) 70000
Answer: d) 70000
Explanation: Capacity of a packet of milk = 350 millilitres
Total amount of milk = 24.5 kilolitres
= 24.5 × 1000 litres
= 24500 litres
= 24500 × 1000 millilitres
= 24500000 millilitres
Number of packets = 24500000350 = 70000
Example 2: An oil drum of 45 decalitres is capable of filling 30 bottles of 1 litre, 23 bottles of 2 litres, 14 bottles of 2.5 litres, 26 bottles of 3 litres, 15 bottles of 5 litres, 11 bottles of 10 litres and some bottles of half a litre. How many bottles of half litre can be filled from the remaining amount of oil?
a) 86
b) 172
c) 76
d) 152
Answer: d) 152
Explanation: Total capacity of an oil drum = 45 daL
= 45 × 10 L
= 450 L
Total Capacity of 30 bottles of 1 litre = 30 × 1 = 30 L
Total capacity of 23 bottles of 2 litres = 23 × 2 = 46 L
Total capacity of 14 bottles of 2.5 litres = 14 × 2.5 = 35 L
Total capacity of 26 bottles of 3 litres = 26 × 3 = 78 L
Total capacity of 15 bottles of 5 litres = 15 × 5 = 75 L
Total Capacity of 11 bottles of 10 litres = 11 × 10 = 110 L
Volume of remaining oil = 450 − (30 + 46 + 35 + 78 + 75 + 110)
= 450 − 374
= 76 L
Number of bottles of half a litre can be filled from 1 litre = 2
Number of bottles of half a litre can be filled from 76 litres = 2 × 76 = 152
CREST Olympiads has launched this initiative to provide free reading and practice material. In order to make this content more useful, we solicit your feedback.
Do share improvements at info@crestolympiads.com. Please mention the URL of the page and topic name with improvements needed. You may include screenshots, URLs of other sites, etc. which can help our Subject Experts to understand your suggestions easily.