MEASUREMENTVolume & Capacity

Converting cubic unitsConverting between cubic units means the base conversion factor

must be cubed.

1 cm3 = 1000 mm3

(1cm 1cm ⨯ ⨯1cm)

(10mm 10mm ⨯ ⨯10mm)

Example

Volume of Prisms

Volume = Area of cross section × Length

Area

L

The volume of a 3-d object is the amount of 3-d space it occupies.

Measured in cubic units i.e. cm3 or m3.

Volumes of prisms and cylinders

Volumes of prisms and cylinders

Volumes of pyramids and cones

Volumes of pyramids and spheres

Volumes of Composite SolidsAs with area, to find the volume of a composite solid, divide it into familiar solids, then find the volume of each, and add/subtract as necessary.

Example

320cm3

Volumes of Composite Solids

Examples

31616cm3 235.6cm3

An excavator is digging a drainage trench. The shape is twice as wide as it is deep. This particular trench has a width across the top of 3.2 m and a length 245 m. What is the best model to calculate the volume of material removed?

What volume of material must be moved to make this trench?

1.6 m

3.2 m

* diagram not to scale

Investigate 2 possible models that could be used to approximate the shape shown. If the digger removes a bucketful of clay at the rate of 2 scoops per 90s, and each scoop holds 2.5m3, how long will it take for each model.

Which model would be better and why?? 1.2 m

In class experiment: investigating volume and capacity

Liquid Item

Volume 1m 1m ⨯ ⨯1m = 1 m3

#mls ≈ #mls ≈

Capacity #L’s = = 1 L

355 1000 1000

= =

Mass #gms ≈ 355 #gms ≈

= 1 kg

1000 #kgs = 1000 = 1t

Liquid Volume (Capacity)There are 2 ways in which we measure volume: Solid shapes have volume measured in cubic units (cm3, m3 …) Liquids have volume measured in litres or millilitres (mL)

Metric system – Weight/volume conversions for water

Weight Liquid Volume Equivalent Solid Volume

1 gram 1 mL 1 cm3

1 kg 1 litre 1000 cm3

Example

600 ml = $ 0.83/0.6 L= $ 1.383 / L

1 L = $ 1.39/ L

2 L = $ 2.76/ 2 L= $ 1.38 / L 1

2

3

S.A. = 2(55 × 42) + 2(18 × 42) + (55 x 18)

55 cm

42 cm

a.) Calculate the area of glass required for the fish tank

b.) Calculate the volume of water in the tank. Give your answer to the nearest litre

= 7122 cm2

Vtank = 55 × 42 × 18= 41580 cm3

Vwater = 4/5 (41580)= 33264 cm3 = 33 L

Example

Homework 3d Prisms/Cylinders: Exercise K: Pages 179-181Pyramids/Spheres: Exercise L: Page 182Composite Solids: Exercise M: Pages 183-184