smc-685-30-Ratios and geometry

Measurement, NAP-G4-CA32

The rectangular prism, shown below, is cut in half to form 2 equal cubes.

What is the ratio of the surface area of the rectangular prism to one of the cubes?

`3 : 5`	`5 : 3`	`1 : 2`	`2 : 1`

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`5 : 3`

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`text(S.A. of rectangular prism)`

`= 2 xx (h xx h) + 4 xx (2h xx h)`

`= 2h^2 + 8h^2`

`= 10 h^2`

`text(S.A. of cube)`

`= 6 xx (h xx h)`

`= 6h^2`

`:.\ text(Ratio of rectangular prism to cube)`

`= 10h^2 : 6h^2`

`= 5 : 3`

Mark and Jim have property sizes as shown in the table below:

What is the ratio of the land area of Mark's property to Jim's property.

`2:1`	`5:2`	`200:1`	`250:1`	`4000:1`

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`200:1`

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`text(1 km²)`	`= 1000\ text(m × 1000 m)`
	`= 1\ 000\ 000\ text(m²)`