Area, Volume & Circle Geometry

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Corbett MathsArea and circumference of circles

Corbett MathsVolume of cylinders, cones and spheres

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GCSE Maths TutorVolume and Surface Area of a Sphere | Grade 5 Crossover Playlist | GCSE Maths Tutor

Key facts & methods

2D areas and perimeters

Rectangle: A = lw. Triangle: A = ½bh. Parallelogram: A = bh. Trapezium: A = ½(a+b)h.
Circle: circumference = 2πr = πd. Area = πr².
Sector: arc length = (θ/360) × 2πr. Area = (θ/360) × πr².
Segment area = sector area − triangle area.
Convert between units: 1 m² = 10,000 cm². 1 cm² = 100 mm².

3D volumes and surface areas

Cuboid: V = lwh. Prism: V = cross-section area × length.
Cylinder: V = πr²h. Surface area = 2πr² + 2πrh.
Cone: V = ⅓πr²h. Curved surface area = πrl (l = slant height).
Sphere: V = (4/3)πr³. Surface area = 4πr².
Pyramid: V = ⅓ × base area × height.
Convert: 1 m³ = 1,000,000 cm³. 1 litre = 1000 cm³.

Exam questions — 5 questions · 12 marks · Edexcel 4MA1 style

1 markSector area4MA1 style

A sector has radius 8 cm and angle 135°. What is its area?

A 75.4 cm²

B 150.8 cm²

C 50.3 cm²

D 301.6 cm²

3 marksVolume of cylinder and cone4MA1 style 🔢 Calculator

A cone has radius 5 cm and height 12 cm. (a) Calculate the volume. (b) Calculate the slant height and curved surface area. Leave answers in terms of π where appropriate. (3 marks)

Hint: (a) V = ⅓πr²h. (b) Slant height uses Pythagoras: l = √(r²+h²). Then curved SA = πrl.

+30 XP

4 marksComposite shape problem4MA1 style 🔢 Calculator

A swimming pool is a prism with trapezoidal cross-section. The trapezium has parallel sides 1.2 m and 2.5 m, and width 25 m. The pool is 50 m long. Calculate the volume of water needed to fill it. (4 marks)

Hint: Volume of prism = cross-sectional area × length. Cross-section is a trapezium: A = ½(a+b)h.

+40 XP

3 marksSphere and cylinder combined4MA1 style 🔢 Calculator

A hemisphere of radius 4 cm is attached to a cylinder of the same radius and height 10 cm. Calculate the total volume and total surface area. (3 marks)

Hint: Volume: hemisphere = ½ × (4/3)πr³. Cylinder = πr²h. Surface area: flat base of cylinder + curved cylinder + curved hemisphere (no flat circle at top — it joins the hemisphere).

+30 XP

1 markVolume conversion4MA1 style

A container holds 2.5 litres. What is this in cm³?

A 250 cm³

B 2500 cm³

C 25,000 cm³

D 0.25 cm³

Area, Volume & Circle Geometry

2D areas and perimeters

3D volumes and surface areas

Module complete! 🎉