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5.3 Measuring mass or weight
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5.5 Measuring and monitoring temperature
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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 \(\text{200}\) \(\text{ml}\).
As with length and weight, we use different containers or instruments to measure the volume of different quantities of liquid or dry ingredients. Some examples are given below:
| 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.
An urn of boiling water in an office has a capacity of \(\text{20}\) litres.
After everyone has their morning tea, there are only \(\text{6}\) litres of water left in the urn.
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 \(\text{10}\) \(\ell\).
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?
A six pack of soft drinks contains \(\text{6}\) cans of \(\text{330}\) \(\text{ml}\) each. What is the total volume of soft drink in a six pack? Give your answer in litres.
\(\text{6}\) \(\times\) \(\text{330}\) \(\text{ml}\) = \(\text{1 980}\) \(\text{ml}\) = \(\text{1,98}\) litres
A large juice container has a capacity of \(\text{30}\) litres.
If the container is \(\text{75}\%\) full, calculate the amount of juice in the container in litres.
\(\text{30}\) litres \(\times\) \(\text{0,75}\) = \(\text{22,5}\) litres
How many \(\text{300}\) \(\text{ml}\) cups of juice can you fill (to the top)?
\(\text{22,5}\) litres \(\div\) \(\text{300}\) \(\text{ml}\) = \(\text{2 250}\) \(\text{ml}\) \(\div\) \(\text{300}\) \(\text{ml}\) = \(\text{6,8}\) cups = \(\text{6}\) full cups.
Jonathan uses the following recipe to make chocolate muffins: \(\frac{\text{2}}{\text{3}}\) cup of baking cocoa \(\text{2}\) large eggs \(\text{2}\) cups of flour \(\frac{\text{1}}{\text{2}}\) cup of sugar \(\text{2}\) teaspoons of baking soda \(\text{1}\frac{\text{1}}{\text{3}}\) cups of milk \(\frac{\text{1}}{\text{3}}\) cup of sunflower oil \(\text{1}\) teaspoon of vanilla essence \(\frac{\text{1}}{\text{2}}\) teaspoon of salt
If \(\text{1}\) teaspoon = \(\text{5}\) \(\text{ml}\), calculate how much baking soda Jonathan will use. Give your answer in ml.
\(\text{2}\) \(\times\) \(\text{5}\) \(\text{ml}\) = \(\text{10}\) \(\text{ml}\).
Calculate the amount of vanilla essence Jonathan will use in this recipe. Give your answer in ml.
\(\text{1}\) tsp = \(\text{5}\) \(\text{ml}\).
Jonathan does not own measuring cups but he does own a measuring jug calibrated in ml. How many ml of flour does he need? (\(\text{1}\) cup = \(\text{250}\) \(\text{ml}\)).
\(\text{2}\) cups flour \(\times\) \(\text{250}\) \(\text{ml}\) = \(\text{500}\) \(\text{ml}\).
If Jonathan buys a \(\text{100}\) \(\text{ml}\) bottle of vanilla essence, how many times will he be able to use the same bottle, if he bakes the same amount of muffins each time?
\(\text{100}\) \(\text{ml}\) \(\div\) \(\text{5}\) \(\text{ml}\) = \(\text{20}\) times.
The recipe above is used to make \(\text{30}\) muffins. Calculate how many cups of flour Jonathan will need to make \(\text{45}\) muffins.
\(\dfrac{\text{2} \text{ cups flour}}{\text{30} \text{ cupcakes}} = \dfrac{\text{3} \text{ cups flour}}{\text{45} \text{ cupcakes}}\) so he will need \(\text{3}\) cups of flour.
Suppose paraffin is sold at \(\text{R}\,\text{7,80}\) per litre at the local service station.
If you have a paraffin lamp at home that can hold \(\text{500}\) \(\text{ml}\) of paraffin, how many times will you be able to refill the lamp if you buy \(\text{3}\) litres of paraffin?
If petrol costs \(\text{R}\,\text{11,72}\) a litre:
Calculate how many litres you could buy with \(\text{R}\,\text{200}\). Round off your answers to two decimal places.
Thandi is baking cupcakes and the recipe she has requires \(\text{1}\frac{\text{1}}{\text{3}}\) cups of milk.
Calculate how many ml of milk she will need if \(\text{1}\) cup = \(\text{250}\) \(\text{ml}\).
\(\text{1}\frac{\text{1}}{\text{3}}\) cups = \(\frac{\text{4}}{\text{3}}\). \(\frac{\text{4}}{\text{3}} \times \text{250}\) ml = \(\text{333}\) \(\text{ml}\) of milk.
If the recipe is designed to produce \(\text{20}\) cupcakes, calculate the amount of milk required to bake \(\text{30}\) cupcakes. Give your answer in litres.
\(\dfrac{\text{330}\text{ ml}}{\text{20} \text{ cupcakes}} = \dfrac{\text{500}\text{ ml}}{\text{30} \text{ cupcakes}}\). She will need \(\text{500}\) \(\text{ml}\) of milk.
Milk is sold in bottles of \(\text{1}\) litre each for \(\text{R}\,\text{8,50}\) at the local store. Calculate the amount of money Thandi will need to spend on milk to make the \(\text{30}\) cupcakes.
\(\text{1}\) bottle = \(\text{R}\,\text{8,50}\) (she will only use half).
Thabiso decides to sell homemade lemonade. He has made \(\text{5}\) litres of lemonade to sell at the local schools' rugby tournament.
Thabiso will be selling his lemonade in \(\text{250}\) \(\text{ml}\) plastic cups. Calculate the number of cups of lemonade he will be able to sell.
\(\text{5}\) litres = \(\text{5 000}\) \(\text{ml}\). \(\text{5 000}\) \(\text{ml}\) \(\div\) \(\text{250}\) \(\text{ml}\) = \(\text{20}\) cups.
If he sells the lemonade at \(\text{R}\,\text{5}\) per cup, how much money will he make from the lemonade? (Assume that he sold all of his lemonade).
\(\text{20}\) cups \(\times\) \(\text{R}\,\text{5}\) = \(\text{R}\,\text{100}\)
If it cost Thabiso \(\text{R}\,\text{120}\) to make the lemonade, how many cups would he need to sell (at \(\text{R}\,\text{5}\) each) before he's made back the money he spent?
\(\text{R}\,\text{120}\) \(\div\) \(\text{R}\,\text{5}\) = \(\text{24}\). He would need to sell \(\text{24}\) cups just to recoup his costs.
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5.3 Measuring mass or weight
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5.5 Measuring and monitoring temperature
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