smc-3153-50-Volume

Measurement, NAP-K3-CA33 SA

A horse trough is in the shape of a rectangular prism, pictured below.

What is the capacity of the horse trough in litres?

litres

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`160`

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`text(Convert all measurements to metres.)`

Two identical solid cubes are placed at the bottom of a fish tank.

The fish tank is then completely filled, as shown below.

What is the volume of the water that surrounds the cubes?

Give your answer in cubic centimetres.

cm³

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`185\ 250\ text(cm)^3`

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`text(Volume of tank)`	`= 80 xx 60 xx 40`
	`= 192\ 000\ text(cm)^3`

`text(Volume of cubes)`	`= 2 xx 15 xx 15 xx 15`
	`= 6750\ text(cm)^3`

`:.\ text(Volume of water)`	`= 192\ 000 – 6750`
	`= 185\ 250\ text(cm)^3`

A small shipping container is the shape of a rectangular prism.

The volume of the small shipping container is 6 cubic metres.

A large shipping container has dimensions that are double the dimensions of the small shipping container.

What is the volume of the large shipping container?

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`text(48 cubic metres)`

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`text(The dimensions of the small container could be:)`

STRATEGY: Doubling dimensions that satisfy a volume of 6 m³ (although we don’t know the exact dimensions) can be used in this type of question.

`2 xx 3 xx 1 = 6\ text(m³)`

`text(If these dimensions are all doubled:)`

`text(Volume)`	`=4 xx 6 xx 2`
	` = 48\ text(m³)`

Florence used identical cubes to build a rectangular prism.

There were 16 cubes in its base.

She used 80 cubes altogether.

Which of these could be the dimensions of Florence's prism?

`10 xx 1 xx 8`	`2 xx 8 xx 5`	`4 xx 4 xx 10`	`4 xx 8 xx 5`

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`2 xx 8 xx 5`

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`2 xx 8 xx 5`

`=>\ text(The above dimensions have a base that is 16)`

`text{cubes (2 × 8) and require a total of 80 cubes}`

`text{(2 × 8 × 5 = 80).}`