v1 Measurement, STD2 M7 2023 HSC 26

Jo is constructing a concrete border around a rectangular vegetable patch, as shown. The border is 0.6 m wide.

Find the area of the border. (2 marks)
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Jo is preparing concrete using a mix of gravel, sand, and cement in the ratio 5 : 3 : 2 by weight.
Jo needs 2 tonnes of concrete in the correct ratio.
Calculate how many 20 kg bags of cement Jo needs to buy. (3 marks)

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a. `text{Area of outer rectangle} = 6.5 × 4.2 = 27.3\ \text{m}^2`

`text{Area of garden} = 5.3 × 3.0 = 15.9 \ text{m}^2`

`text{Area of border}`	`= 27.3-15.9`
	`=11.4\ text{m}^2`

b. `text{Ratio parts:} \ 5 + 3 + 2 = 10` parts

`text{Total concrete} = 2\ \text{tonnes} = 2000\ \text{kg}`

`text{Each part} = 2000 ÷ 10 = 200\ \text{kg}`

`text{Cement} = 2 \ text{parts} = 2 × 200 = 400\ \text{kg}`

`text{Bags of cement} = 400 ÷ 20 = 20`

`⇒ \ text{Jo needs 20 bags of cement.}`