1.2 Working with formulae and equations

Area of a rectangle = Width x Length

1 cm is 1.0 × 10−2 m
400 cm = 400 × 10−2 m = 4.00 m
Note: 400 could be accurate to 1, 2 or 3 significant figures — 3 significant figures have been kept here after unit conversion.

400cm × 1.2m = 4.00 m × 1.2m = 4.80 m2
However, the least accurate value, 1.2m, is significant to 2 figures only, so the answer should be provided to this accuracy. 4.80 m2 = 4.8 m2 (2 s.f.)

I would start by converting both measurements to be the same. I work in mm so I would convert both to mm i.e. 400cm = 4000mm and 1.2m = 12000mm.

Then I would multiply 4000 x 12000 = 48000mm2. I would then round this number down into m2 by dividing 48000/1000 = 4.8m2

To calculate the voltage difference, you will need to use Ohm's law, which is:

Voltage (V) = Current (A) x Resistance (Ohm)

V=IR

0.020 A = 2.0 × 10−2 A

V = IR = 2.0 × 10−2 A × 330 Ω = 660 × 10−2 V

660 × 10−2 V = 6.60 × 102 × 10−2 V

When multiplying powers of 10, add the powers.
6.60×102 ×10−2V=6.60V

The most accurate value given is 0.020A, which has two significant figures, so change the answer to this level of accuracy. Answer: 6.60 V = 6.6 V (2 s.f.)

I would start by moving the decimal place of the 0.020 A so that it reads as 2.0. I would then multiply this by 330 Ohms = 660 Ohms.

I would then move the decimal point back two places = 6.6. This becomes Volts as we follow the formula V=IR. Therefore 6.6V.

Volume of a cylinder = πr2h

12 mm = 12 × 10−3 m = 1.2 × 10−2 m

volume of a cylinder = πr2h = π(1.2 × 10−2)2 × 0.2
π(1.2 × 10−2)2 × 0.2 = π(1.44 × 10−4) × 0.2 = 0.90478 × 10−4 (5 d.p.)

The values provided at the start of the calculation are accurate to 2 significant
figures, so this answer should be given to the same level of significance. Answer: 0.90 × 10−4 (2 s.f.)

I would start by converting the height into mm = 0.2m = 2000mm.

Then volume of a cylinder is πr2h = π x (12x12) x 2000 = 904788.684mm3

I would then divide this total by 1000 to convert into m3 = 904.779. 

This should then be refined to 904.78m3 or 0.90 × 10−4 (2 s.f.)

Circumference of external curve as a full circle C = π x D

180 degree curve with a radius of 250mm = Diameter 500mm

C (Circumference) = π x 500 (or 2 x π x 250) = 1570.796. This is rounded up to 1571 (whole number).

Length of 180 degrees of external curve = 180/360 x 100 = 50% of full circle circumference or 1/2.

So Curve A = 1571 / 2 = 785.5mm

The question says write your answer to the nearest whole number, so the length of the external curve A = 786mm. 

Anything below 0.5 i.e. 0.499999 is rounded down and anything above 0.5 is rounded up.

1500 + 786 + 600 + 125 + 700 = 3711mm

3711 (total length) x 7 (nmber of veneers) x 2 (two sides of chair) = 51954mm. 

This could also be written as 51.95m

Area of veneer = Width x Length

Veneer is 100mm wide and the question is using metre square as the unit of measurement

Width is 100mm = 10cm = 0.1m (100cm in 1 metre)

Length from previous answer is 51.95m

0.1 (width) x 51.95 (length) = 5.195m2

Plus 15%

This can be done one of two ways

5.195 x 1.15 = 5.97425 = 5.97m2 or

5.195 x 15 = 77.925. 77.925 / 100 = 0.77925 (15%). 0.77925 (15%) + 5.195 (length) = 5.97425. 5.97m2 (2 decimal places)

Now you have the total length including the additional 15% you need to work out the total cost for 5.97m2 at 20.45GBP per m2.

5.97 x 20.45 = 122.09GBP (122 pounds and 9 pence)