Measurement, NAP-J4-CA39 SA
Measurement, NAP-D4-NC30 SA
When 1 mm of rain falls on 1 m² of a pool, 1 litre of water is collected.
A pool of what surface area is needed to collect 6000 litres from a rainfall of 15 mm?
m² |
Aussie Maths & Science Teachers: Save your time with SmarterEd
A grain silo is in the shape of a cylinder.
The silo has a diameter of 10 metres.
Grain is poured into an empty silo at a rate of 4 cubic metres per minute.
Approximately how long will it take to completely fill the silo?
`1 3/4\ text(hours)` | `2 1/2\ text(hours)` | `4\ text(hours)` | `16\ text(hours)` |
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`4\ text(hours)`
`text(Volume of cylinder)`
`= pi xx r^2 xx h`
`= pi xx 5^2 xx 12`
`~~ 942\ text(m³)`
`:.\ text(Time to fill silo)`
`~~ 942 ÷ 4`
`~~ 235\ text(mins)`
`~~ 4\ text(hours)`
A rectangular prism is made by using 6 identical triangular prisms.
What is the volume of one rectangular prism, in cubic centimetres?
cubic centimetres |
`37 200 text(cm³)`
`text(Volume of rectangular prism)`
`= 62 xx 50 xx 72`
`= 223\ 200\ text(cm³)`
`:.\ text(Volume of 1 triangular prism)`
`= 223\ 200 ÷ 6`
`= 37\ 200\ text(cm³)`
When 1 mm of rain falls on 1 m² of a pool, 1 litre of water is collected.
A pool of what surface area is needed to collect 6000 litres from a rainfall of 15 mm?
m² |
`400`
`text(If 15 mm of rain falls on 1 m²)`
`=> 15\ text(litres collected)`
`:.\ text(Surface Area of pool needed)`
`= 6000/15`
`= 400\ text(m²)`
The flask pictured below can hold up to 100 mL of water.
How much water is in the flask?
`60\ text(mL)` | `70\ text(mL)` | `80\ text(mL)` | `90\ text(mL)` |
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`text(80 mL)`
`text(Flask is fully filled until the 60 mL mark.)`
`text(Flask is half filled between 60-100 mL marks.)`
`:.\ text(Volume of water in the flask)`
`=60 + (1/2 xx 40)`
`=80\ text(mL)`
Tom cut a tennis ball into two halves.
The following calculation gives the approximate volume of one half of the ball in cm³.
`text(Volume) = 1/2 xx 4/3 pi xx r^3`
What volume does the calculation give, to the nearest cm³, where `r` is the radius of the ball?
cm³ |
`90\ text(cm³)`
`V` | `= 1/2 xx 4/3 pi xx 3.5^3` |
`= 89.79…` | |
`= 90\ text(cm³)` |
A shoebox is square at each end and twice as long as it is high, as shown in the diagram.
Which of these is the closest estimate for the number of cubes that would fill the box?
`16` | `60` | `130` | `500` |
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`130`
`text(The box front is around 4 cubes wide and 4 cubes high.)`
`text(Estimated cubes that could fit)`
`=h xx h xx (2h)`
`= 4 xx 4 xx (4 + 4)`
`= 16 xx 8`
`= 128`
`:. 130\ text(is the closest.)`