smc-902-65-Rates and geometry

Number, NAP-F3-CA31 SA

Gary used 4 litres of paint to paint a wall.

The wall was a rectangle 2 metres high and 3 metres wide.

How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 5 metres wide?

litres

Show Answers Only

`10`

Show Worked Solution

`text(Area of smaller wall)`

`= 2 xx 3`

`= 6\ text(m²)`

`text(S)text(ince 4 litres of paint are needed to)`

`text(paint the small wall:)`

`=>\ text(Paint needed for 1 m²)`

`= 4/6`

`= 2/3\ text(litre)`

`=>\ text(Area of larger wall)`

`= 3 xx 5`

`= 15\ text(m²)`

`:.\ text(Paint needed)`	`= 15 xx 2/3`
	`= 10\ text(litres)`

Number, NAP-C3-CA29 SA

Natalie is building a brick wall 9 metres high.

The height of a column of 15 bricks is 1.8 metres as shown.

How many bricks will Natalie need for a wall 9 metres high?

Show Answers Only

`75\ text(bricks)`

Show Worked Solution

`text(Let)\ \ h=\ text(height of 1 brick)`

`15 xx h`	`=1.8`
`h`	`= 1.8/15`
	`=0.12\ text(m)`

`text(If the wall is 9 metres high,)`

`:.\ text(Number of bricks needed)`

`=9/0.12`

`=75\ text(bricks)`

Number, NAP-F3-NC31 SA

Adam is laying tiles in the pattern shown below.

He uses three white tiles for every four gray tiles as shown.

He uses a total of 133 tiles.

How many gray tiles does he use?

Show Answers Only

`76`

Show Worked Solution

`text(In every 7 tiles, 3 are white and 4 are black.)`

`=> 133/7 = 19\ text(groups of 7 tiles)`

`:.\ text(Number of gray tiles)`

`= 19 xx 4`

`= 76`

Number, NAP-G3-NC30

Five people had sticks of different lengths.

Each person measured a 30 metre interval by counting how many stick lengths it took.

The results were put into the table below.

Which person had a stick that was 60 centimetres long?

John	Caroline	Paul	Simon	Ken

Show Answers Only

`text(Simon)`

Show Worked Solution

`text(Stick lengths) xx 60\ text(cm)`	`=30\ text(m)`
	`=3000\ text(cm)`
`text(Stick lengths)`	`=3000/60`
	`=50`

`:.\ text(Simon has the 60 cm stick.)`

Geometry, NAP-C3-NC27 SA

Elloise is taking a ride on a ferris wheel.

It takes her 5 minutes to complete a full lap.

What angle does the Ferris wheel turn through in 75 seconds?

Show Answers Only

`90`

Show Worked Solution

`text(5 minutes = 300 seconds)`

`:.\ text(Angle turned through)`	`=75/300 xx 360°`
	`=1/4 xx 360°`
	`=90°`