Flashcards · 0580 · Topic 5

Mensuration flashcards

30 cards on Topic 5, subtopics 5.1 to 5.5. Pick a subtopic or study them all.

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Converting units: when do you multiply and when do you divide?: To a smaller unit (km → m): there are more of them, so multiply. To a larger unit (ml → l): there are fewer of them, so divide.
How many cm² in 1 m², and mm² in 1 cm²?: 1 m² = 100² = 10 000 cm² 1 cm² = 10² = 100 mm² Square the length factor for area.
How many cm³ in 1 m³, and mm³ in 1 cm³?: 1 m³ = 100³ = 1 000 000 cm³ 1 cm³ = 10³ = 1000 mm³ Cube the length factor for volume.
Link between volume and capacity: 1 cm³ = 1 ml, so 1000 cm³ = 1 litre and 1 m³ = 1000 litres.
Convert 0.36 m² to cm²: 0.36 × 10 000 = 3600 cm²
A tank is 1.2 m by 80 cm by 50 cm. How many litres does it hold?: 120 × 80 × 50 = 480 000 cm³ 480 000 ÷ 1000 = 480 litres

Area of a rectangle, a triangle and a parallelogram: Rectangle: length × width. Triangle: ½ × base × perpendicular height. Parallelogram: base × perpendicular height.
Area of a trapezium: ½(a + b)h, where a and b are the parallel sides and h is the perpendicular distance between them. You must learn it: only the triangle formula is given.
A trapezium has parallel sides 5 cm and 9 cm and height 4 cm. Find its area.: ½ × (5 + 9) × 4 = 28 cm²
Perimeter of a rectangle: 2(length + width): the total distance round the edge.
Exam trap: area of a parallelogram: Using the slanted side instead of the perpendicular height. The height must be at right angles to the base.

Circumference and area of a circle: Circumference = 2πr = πd Area = πr²
Arc length and sector area for a sector of angle θ° and radius r: Arc length = (θ/360) × 2πr Sector area = (θ/360) × πr²
Find the area of a quarter circle (90° sector) of radius 4 cm, in terms of π: (90/360) × π × 4² = ¼ × 16π = 4π cm² (≈ 12.6 cm²)
Find the perimeter of a 60° sector of radius 6 cm: Arc = (60/360) × 2π × 6 = 2π Perimeter = arc + two radii = 2π + 12 ≈ 18.3 cm
The minor angle of a sector is 80°. What angle do you use for the major sector?Extended: 360° − 80° = 280°.
Find the area of a sector of radius 8 cm and angle 110°Extended: (110/360) × π × 8² = 61.4 cm² (3 s.f.)

Volume of a prism, and of a pyramid: Prism: area of cross-section × length. Pyramid: ⅓ × base area × perpendicular height.
Volume and total surface area of a closed cylinder: V = πr²h Total surface area = 2πrh + 2πr² (curved surface plus two circular ends).
A cylinder has radius 5 cm and height 8 cm. Find its volume and total surface area in terms of π.: V = π × 25 × 8 = 200π cm³ SA = 2π × 5 × 8 + 2π × 25 = 80π + 50π = 130π cm²
Volume and curved surface area of a cone: V = ⅓πr²h, where h is the perpendicular height. Curved surface area = πrl, where l is the slant height.
A cone has radius 3 cm and slant height 5 cm. Find its volume.: Perpendicular height: h² = 5² − 3² = 16, so h = 4. V = ⅓ × π × 9 × 4 = 12π ≈ 37.7 cm³
Volume and surface area of a sphere: V = (4/3)πr³ Surface area = 4πr²
Volume and surface area of a cuboid 8 cm × 5 cm × 3.5 cm: V = 8 × 5 × 3.5 = 140 cm³ SA = 2(40 + 28 + 17.5) = 171 cm²

How do you find the area or volume of a compound shape?: Split it into simple shapes. Add the parts joined on and subtract any parts removed.
A semicircle of diameter 6 cm is cut from a 10 cm × 6 cm rectangle. Find the remaining area.: 60 − ½ × π × 3² = 60 − 14.14 = 45.9 cm² (3 s.f.)
Area of a semicircle of radius r: ½πr². Use the radius, not the diameter.
Perimeter of a compound shape: Add only the lengths round the outside. Leave out any edges where two parts join.
Volume and curved surface area of a hemisphere (half a sphere): Volume = ½ × (4/3)πr³ = (2/3)πr³ Curved surface area = ½ × 4πr² = 2πr² (add πr² for the flat face).
How do you find the volume of a frustum of a cone?Extended: Volume of the whole cone minus the volume of the small cone cut off the top.