7) Answer this
2 points
3) How much water should you pour out from each jug to drop down the water level to 300 mL?
b)
ml
mt
325 & 1500 ml
300 & 1400 ml
450 & 300 ml
Answers
Measuring volume
Volume is a measurement of how much space an object takes up (e.g. \(\text{600}\) \(\text{ml}\) of water). Capacity is a measure of how much liquid a container can hold when its full. (e.g. a \(\text{2}\) litre bottle). For example, if you have a \(\text{500}\) \(\text{ml}\) bottle of cola, with \(\text{200}\) \(\text{ml}\) of cola left inside it, the capacity of the bottle is \(\text{500}\) \(\text{ml}\), while the volume of cola inside it is \(\text{200}\) \(\text{ml}\).
Measuring spoons come in different standard sizes or capacities, including a teaspoon (\(\text{5}\) \(\text{ml}\)) and a tablespoon (\(\text{15}\) \(\text{ml}\)). Some sets of spoons also include \(\frac{\text{1}}{\text{2}}\) and \(\frac{\text{1}}{\text{4}}\) teaspoons.
Measuring cups also come in standard capacities, including \(\text{1}\) cup (\(\text{250}\) \(\text{ml}\)), \(\frac{\text{1}}{\text{2}}\) a cup (\(\text{125}\) \(\text{ml}\)) and \(\frac{\text{1}}{\text{4}}\) cup (\(\text{63}\) \(\text{ml}\)).
Measuring jugs come in many different sizes, but the most common capacity is \(\text{1}\) litre. The measuring jug on the left gives measurements in litres and millilitres. It has a capacity of \(\text{1}\) \(\ell\).
Flasks, like measuring jugs, come in different capacities. They usually don't come with any calibrated measurements, (just a capacity measurement) so the only way to know what the volume of liquid inside a flask is, is to pour it out into a measuring jug.
The capacity of an average household bucket is \(\text{10}\) litres. Some buckets have litre markings on the inside that enable you to measure off a volume of liquid less than \(\text{10}\) litres. (This is only accurate to the nearest litre though!)
The capacity of a wheelbarrow is usually about \(\text{170}\) litres.
As we learned in Chapter 3, it is possible to estimate the quantities of a substance that we need - for example heaped teaspoons. Another common way of estimating is using a fraction of a standard quantity, for example a quarter teaspoon of salt, or half a brick of butter.
WORKED EXAMPLE 7: MEASURING VOLUME
An urn of boiling water in an office has a capacity of \(\text{20}\) litres.
If it is filled to maximum capacity, calculate the number of \(\text{250}\) \(\text{ml}\) cups that can be shared from it.
After everyone has their morning tea, there are only \(\text{6}\) litres of water left in the urn.
How much water is this in ml?
How many \(\text{250}\) \(\text{ml}\) cups of water are left in the urn now?
What percentage of the urn still has water in it?
Jabu is building a new flower bed and is using a bucket to carry soil from another part of the garden to the new bed. He knows his bucket has a capacity of \(\text{10}\) \(\ell\).
If he has \(\text{300}\) \(\ell\) of soil that needs to be moved, and for each trip he fills the bucket to the top with soil, how many trips will Jabu have to make with the bucket to move all the soil?
Jabu decides that \(\text{10}\) litres of soil is too heavy to carry. How many trips will he have to make to move all the soil if he only fills the bucket with \(\text{7}\) litres of soil at a time?
Jabu's friend Matthew arrives with his wheelbarrow and a spade. He suggests that Jabu should rather move the soil using the wheelbarrow. If the wheelbarrow has a capacity of \(\text{150}\) litres and they fill it to the brim, how many trips will Jabu have to make to move all the soil?
Dorothy goes hiking with her friends every Sunday morning. She always takes a flask of tea. She knows that the lid of the flask (which doubles as a cup) can hold \(\text{200}\) \(\text{ml}\) of water. If she can get five and a half cups of tea out of the flask, calculate the capacity of the flask, in litres.
\(\text{20}\) litres = \(\text{20 000}\) \(\text{ml}\) \(\text{20 000}\) \(\text{ml}\) \(\div\) \(\text{250}\) \(\text{ml}\) = \(\text{80}\) \(\text{80 250}\) \(\text{ml}\) cups can be poured from the urn.
\(\text{6}\) \(\ell\) = \(\text{6 000}\) \(\text{ml}\)
\(\text{6 000}\) \(\text{ml}\) \(\div\) \(\text{250}\) \(\text{ml}\) = \(\text{24}\) There are \(\text{24}\) cups of water left in the urn.
\(\frac{\text{6}\text{ ℓ}}{\text{20}\text{ ℓ}} \times \text{100} = \text{30}\%\) The urn is \(\text{30}\%\) full.
\(\text{300}\text{ ℓ} \div \text{10}\text{ ℓ}\) = \(\text{30}\) trips.
\(\text{300}\text{ ℓ} \div \text{7}\text{ ℓ} = \text{42,8}\). Jabu can't make \(\text{0,8}\) of a trip so we round this up to \(\text{43}\) trips (even though the bucket won't have \(\text{7}\) litres of soil in it for the last trip).
\(\text{300}\text{ ℓ} \div \text{150}\text{ ℓ}\) = \(\text{2}\) trips.
\(\text{200}\) \(\text{ml}\) \(\times\) \(\text{5,5}\) cups = \(\text{1 100}\) \(\text{ml}\) = \(\text{1,1}\) \(\ell\). The capacity of her flask is \(\text{1,1}\) litres.
Step-by-step explanation: