Geometry

Vocabulary flashcards summarising essential shapes, formulas and test-taking strategies for the UCAT Quantitative Reasoning section.

Common 2-D Shapes in UCAT

Circles, rectangles (including squares) and triangles, which can be used to break down more complex figures.

Common 3-D Shapes in UCAT

Cubes, cuboids, cylinders (frequent) and occasionally cones and spheres.

Diameter Formula

d = 2r (twice the radius).

Circumference Formula

C = πd = 2πr (perimeter of a circle).

Area of a Circle Formula

A = πr² (space enclosed by a circle).

Pi (π) Rule in UCAT

Use the given value; if none is provided, assume 3.14 for calculations.

Area of Triangle

A = ½ × base × height.

Pythagoras’ Theorem

a² + b² = c² for right-angled triangles, where c is the hypotenuse.

Quadrilateral Split Trick

Any four-sided figure can be divided into two triangles by drawing one diagonal.

Prism

3-D solid with a uniform cross-section (base) extended through its height.

Volume of a Prism

V = base area × height (applies to cubes, cuboids, cylinders, triangular prisms, etc.).

Volume of a Cube

V = s³, where s is the side length.

Volume of a Cuboid

V = l × w × h (product of its three dimensions).

Volume of a Cylinder

V = πr²h (base area of circle × height).

Volume of a Sphere

V = 4⁄3 πr³ (often provided in UCAT data).

Volume of a Cone

V = ⅓ πr²h (one-third the volume of a cylinder with same base and height).

Surface Area of a Prism

SA = 2 × base area + (base perimeter × height).

Surface Area of a Cube

SA = 6s² (six equal square faces).

Surface Area of a Cuboid

SA = 2(lw + wh + lh) – sum and double the three distinct rectangular faces.

Shape-Breakdown Strategy

Solve complex figures by decomposing them into circles, rectangles/squares or triangles.

Timing Strategy in QR

Plan steps mentally; flag or estimate on lengthy geometry items to avoid leaving answers blank.