Geometric Bites

Scale drawings are useful for representing large real-life objects and areas using smaller measurements. When calculating an area from a scale drawing, the scale factor must be squared because area is two-dimensional. Question – Area of a Park from a Scale Drawing A map has a scale of 1 : 40 000 . A rectangular park is shown on the map as measuring 5.8 cm by 4.4 cm . Calculate the area of the park in real life, giving the answer in km² to 3 significant figures . Working 1 : 4 × 10⁴ 5.8 : 5.8 × 4 × 10⁴ 4.4 : 4.4 × 4 × 10⁴ Area of park in real life: 5.8 × 4.4 × 4² × (10⁴)² cm² = 408.32 × 10⁸ cm² 1 m = 100 cm = 10² cm 1000 m = 1 km = 10⁵ cm 1 cm = 10⁻⁵ km (1 cm)² = (10⁻⁵ km)² 1 cm² = 10⁻...

Density describes how much mass is contained within a particular volume. The relationship between density, mass and volume can be expressed using one formula, which can then be rearranged depending on the quantity that needs to be found. Density Density is calculated by dividing mass by volume: Density = mass / volume d = m / v What the Symbols Mean d = density m = mass v = volume Finding Volume Start with the density formula: d = m / v ⇒ dv = m v = m / d Volume = mass / density Finding Mass Starting again with: d = m / v ⇒ dv = m ...

These examples practise converting units of area and volume, using powers of 10, writing values in standard form, and applying the pressure formula. Particular care is needed because area conversions are squared and volume conversions are cubed. Question 1(a) – Converting m² to cm² Convert 2.3 m² into cm² . Working Convert 2.3 m² into cm². 1 m = 10² cm 2.3 × (10² cm)² = 2.3 × 10⁴ cm² Answer: 2.3 × 10⁴ cm² Question 1(b) – Converting mm³ to cm³ Convert 400 mm³ into cm³ . Working Convert 400 mm³ into cm³ 10 mm = 1 cm 1 mm = 10⁻¹ cm 400 × (10⁻¹ cm)³ = 400 × 10⁻³ cm³ = 4 × 10² × 10⁻³ cm³ = 4 × 10⁻¹ cm³ Answer: 4 ×...