Page 55 - Physics

Measurement

Measurements of volume of a solid
(a) Determining the volume of
regular solid objects 5 cm
Dimensions of a solid with regular shape
such as a cube, a cylinder or a sphere, can
be measured and the appropriate formula 14 cm
is used to calculate its volume. Figure 2.34
For example; Solution
Volume (V) of a rectangular block = Given, π = 3.14, r = 5 cm and h = 14 cm

length (l) × height (h) × width (w). For Formula for calculating volume of a
2
a cube, l = h = w, cylinder V = πr h
Volume of a cylinder Substituting in the formula gives,
(
(
2
2
= π × radius,r) × height, h) = πr h V = 3.14 × 5 cm × 5 cm × 14 cm
3
4 = 1 099 cm .
Volume of sphere = πr 3
3
(b) Determining the volume of irregular
Example 2.6 solid objects
Calculate the volume of a rectangular Measuring the volume of an irregular
block, of sides 15 cm, 8 cm and 7 cm, shaped solid object is based on the
shown in Figure 2.33. Archimedes’ principle which states that
‘when an object is completely submerged in
Solution water, it displaces a volume of water equal
to its own volume’. Thus the volume of an
irregular object can be measured using:
7 cm
(i) a measuring cylinder; and
(ii) a eureka can or an overfl ow can.
8 cm
15 cm Measuring the volume of irregular
object using a measuring cylinder
Figure 2.33
Suppose you want to measure the volume
of a small stone. The following steps are
Volume of the block = l × w × h necessary.
= 15 cm × 8 cm × 7 cm = 840 cm .
3
1. Fill a measuring cylinder with about
300 mL of water as illustrated in
Example 2.7 Figure 2.35 (a).

Calculate the volume of the cylinder 2. Carefully measure the initial volume
shown in Figure 2.34, given that π = of water V .
3.14. 1

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