1. MEASUREMENT
Volume & Capacity

2. Converting cubic units
Converting between cubic units means the base conversion factor must be cubed.
Example
1 cm = mm3
(1cm ⨯ 1cm ⨯ 1cm)
(10mm ⨯ 10mm ⨯ 10mm)

3. Volume of Prisms Area Volume = Area of cross section × Length 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.
Area L

4. Volumes of prisms and cylinders

5. Volumes of prisms and cylinders

6. Volumes of pyramids and cones

7. Volumes of pyramids and spheres

8. Volumes of Composite Solids
As 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

9. Volumes of Composite Solids
Examples
31616cm3
235.6cm3

10. What volume of material must be moved to make this trench?
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?
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??
1.6 m
3.2 m
1.2 m
* diagram not to scale

11. In class experiment: investigating volume and capacity
Liquid Item
Volume = =
1m ⨯ 1m ⨯ 1m
= 1 m3
Capacity
#mls ≈
355
#mls ≈
1000
= 1 L
#L’s =
1000
Mass
#gms ≈
#gms ≈
355
1000
= 1 kg
#kgs =
1000
= 1t

12. 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

13. 2 3 1 Example 600 ml = $ 0.83/0.6 L = $ 1.383 / L 1 L = $ 1.39/ L

14. = 33 L Example = 7122 cm2 Vtank = 55 × 42 × 18 = 41580 cm3
a.) Calculate the area of glass required for the fish tank
= 7122 cm2
S.A. = 2(55 × 42) + 2(18 × 42) + (55 x 18)
b.) Calculate the volume of water in the tank. Give your answer to the nearest litre
Vtank = 55 × 42 × 18
= cm3
42 cm
Vwater = 4/5 (41580)
= cm3
= 33 L
55 cm

15. Homework 3d Prisms/Cylinders: Exercise K: Pages Pyramids/Spheres: Exercise L: Page 182 Composite Solids: Exercise M: Pages