smc-3177-65-Rates and geometry

Number, NAP-K4-CA31

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)`

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`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)`

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

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`400`

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`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)`

Paul has a paddock that takes him 56 steps to walk across.

One of his steps is 80 centimetres long.

His younger sister, Caroline, has a step length of 70 centimetres.

How many steps does it take Caroline to walk across the same paddock?

`49`	`56`	`64`	`80`	`100`

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`64`

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`text(Paddock length)`

`= 56 xx 0.8`

`= 44.8\ text(m)`

`:.\ text(Number of Caroline’s steps)`

`= 44.8/0.7`

`= 64`