Back to: O level physics notes uganda

Area is ameasure of the size of a surface. The S.I unit is a squaremetre (m2).

Other units of area include: ๐๐2,๐๐2,๐๐2 ๐.๐ก.๐

**Example 1:**

Convert the following as instructed

(i) 15 mm2 to cm2

(ii) 20 m2 to mm2

(iii) 16.4 mm2 to m2

**Solution**

(i) 15 ๐๐2 ๐ก๐ ๐๐2

(ii) 20 ๐2 ๐ก๐ ๐๐2

**Solution**

(iii) 16.4 ๐๐2 ๐ก๐ ๐2

**Types of areas**

(i) Cross-sectional area

(ii) Surface area

**VOLUME:**

Volume is the space occupied by matter. The S.I unit of volume is cubic metre (m3).

Other units of volume include: ๐๐3,๐๐3,๐๐3,๐๐๐๐๐๐๐๐ก๐๐(๐๐),๐๐๐ก๐๐(๐).๐.๐ก.๐

**Instruments for measuring Volume include:**

- Measuring cylinder
- Volumetric flask
- Burette
- Pipette

**Question:**

A measuring cylinder containing some water stands on a scale pan. A solid ball is lowered into the water. The water level rises from the 30cm3 mark to 40cm3 mark. The scale reading increases from 100g to 180g.

What is the density of the material of the ball?

A. 2.0 gcm-3. B. 4.5 gcm-3.

B. 8.0 gcm-3. D. 18 gcm-3.

**Example 1:**

Convert the following as instructed

(i) 250 โฆ.3 โฆ. ..3 (โฆโฆ)0.032โฆ.3 โฆ. ..3

(ii) 500โฆ. โฆ. ..3 (โฆ.)10,000 โฆโฆโฆโฆ โฆ. ..3

**Solution**

(i) 250 ๐๐3 ๐ก๐ ๐3

Find the volume

(i) in cm3 [400cm3 ]

(ii) in m3 [0.0004m3]

**Exercise:**

- A cuboid has dimensions 2cm by 10cm. Find its width in metre if it occupies a volume of 80cm3. [ 0.04m]
- (a) Find the volume of water in a cylinder of water radius 7cm if its height is 10cm.[ 1540cm3]
- (b) The volume of the cylinder was 120m3.When a stone was lowered in the cylinder filled with water the volume increased to 15cm3. Find the height of the cylinder of radius 7cm. [0.078 cm]
- A Perspex box has 10cm square base and contains water to a height of 10cm. A piece of rock of mass 600g is lowered gently into the water and the level rises to 12cm. Find the;
- (i) Volume of water displaced by the rock.
- (ii) volume of the rock in ๐๐๐ and ๐๐
- (iii) density of the rock in ๐๐๐โ๐ and ๐๐๐โ๐

**SCIENTIFIC NOTATION AND SIGNIFICANT FIGURES.**

**Scientific notation or Standard form**

A number is in scientific form, when it is written as a vnumber between 1 and 9 which is multiplied by a power of 10. i.e when it is written in the form ๐ร๐๐๐ง.

Where1โคA<10; i.e A lies between 1 and 10 with 1 inclusive but 10 exclusive. n is an integer (โฆ.-2,-1,0,1,2โฆ).

Scientific notation is used for writing down very large and very small measurements.

**Example:**

(i) 598,000,000m = 5.98 x 108 m

(ii) 0.00000087m = 8.7 x 10-7 m

(iii) 60220m = 6.022 x 104 m

**Questions:**

Convert the following to scientific form.

(a) 0.048 = 4.8 x 10-2

(b) 34 = 0.75 = 7.5 x 10-1

(c) 1000 = 1.0 x 103

(d) 8.72 = 8.72 x 100

(e) 18 = 0.125 = 1.25 x 10-1

**Significant figures**

**Decimal Places**

The number of decimal places (dp) is the number of digits to the right end of a decimal point. E.g. the number 3.6420 is given to 4dp.Thus 3.6420 โ 3.642(3dp), 3.6420 โ 3.64(2dp), 3.6420 โ 3.6(1dp), 3 .6420 โ 4 (0dp).

**Significant Figures**

a) None zero digits (1, 2, 3, 4, 5, 6, 7, 8 and 9) are significant figures.

b) Zeros

Leading zeros (i.e. zeros at the left end of a number) i.e zeros before the first significant figure; are not significant figures e.g. 0.000456 (3s.f), 0.017 (2s.f).

Tapped zeros; zeros between significant figures i.e. zeros between non zero digits are significant figures e.g. 6.0037 (5s.f), 0.0100034 (6 s.f).

Trailing zeros (zeros at the right end of a number);

(i) Trailing after a decimal point: These are significant figures. E.g 2.00 (3s.f), 0.0020 (2s.f), 0.0120700 (6s.f)

Normally these values are obtained by using an instrument.

(ii) Trailing before a decimal point: These are NOT significant figures. E.g 20 (1s.f), 2400 (2s.f), 580100 (4s.f)

Normally these values are obtained as a result of rounding off certain numbers to the nearest tens, fifties, hundreds, thousands, ten thousands e.t.c.

For example, if a number 348 is rounded off to 1 s.f, we get 300 and if it`s rounded off to 2 s.f we get 350. The trailing zeros in these approximations (i.e. 300 and 350) are due to rounding off and therefore are not significant.

**Questions**

Write the following to the stated significant figures

a) 28.8 to 3 s.f b) 2/7 to 2 s.f c) 4.027 x10*2 to 3 s.f