smc-7730-20-Capacity/Volume/Mass

Measurement, STD2 M1 2009 HSC 25b v1

The mass of a sample of hungry cat fleas is 0.675 kilograms. There are approximately `1.5 × 10^6` hungry cat fleas in the sample.

In standard form, what is the approximate mass in grams of one hungry cat flea? (2 marks)

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`4.5 xx 10^-4\ text(grams)`

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`text(Convert 0.675 kilograms into grams:)`

`0.675\ text(kg) = 0.675 xx 1000 = 675\ text(g)`

`:.\ text(Mass of 1 flea)`	`= text(mass of sample)/text(# fleas)`
	`= (675)/(1.5 xx 10^6)`
	`= 4.5 xx 10^-4\ text(grams)`

Milly purchases a new container of Gutho's Fertilizer which holds 25 kg.

The container comes with a small cup that holds 350 grams of fertilizer when full.

Milly has 5 pot plants that each receive 1.5 cups of fertilizer on the 1st day of the month and 1 cup each in the middle of the month.

Milly begins using this new container on the first day of October.

In what month will her fertilizer run out? Justify your answer with calculations. (3 marks)

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`text(March)`

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`text(Cups used per month)= 5 xx (1.5 + 1)=12.5`

`text(Fertiliser used per month)= 12.5 xx 350 = 4375\ text(g)`

`text(Total fertilizer available)\ = 35\ text(kg) = 35\ 000\ text(grams)`

`text(Time it will last)= (25\ 000)/4375= 5.71…\ text{months}`

`:.\ text(The container will run out in March.)`

Deirdre purchases a weed killer product that contains 12 litres of solution.

It is used to spray her lawn twice a week. The instructions state:

If Deirdre's lawn is 30 m² in area, how many full weeks will the weed killer last? (2 marks)

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`text(8 full weeks.)`

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`text{Using 100 mL = 0.1 L:}`

`text{Total weekly usage} = 3 xx(0.4+0.3) = 2.1\ text{litres}`

`text{Total solution} = 18\ text{L}`

`text{Weeks it will last} = 18/2.1=8.57…`

`:.\ text{The bottle will last 8 full weeks.}`