Civil Service Exam (Subprofessional) Numerical Ability — Geometry — Perimeter, Area, Circumference & VolumeFlash Cards

What is perimeter and how is it calculated?

Perimeter is the total distance around the boundary of a closed shape. It is calculated by adding all the side lengths together. For example, a rectangle with length 8cm and width 5cm has perimeter = 2(8) + 2(5) = 26cm. Think of it as the length of fence needed to enclose a piece of land.

Square with side length 12 meters

Perimeter = 4s = 4(12) = 48 meters Area = s² = 12² = 144 square meters Remember: For squares, all sides are equal, so perimeter is 4 times one side, and area is side squared.

What is the difference between area and perimeter?

Perimeter measures the distance AROUND a shape (linear measurement in units like cm, m). Area measures the space INSIDE a shape (square measurement in units like cm², m²). Example: A room's perimeter is the baseboard length needed; area is the floor tiles needed.

Rectangle: Length = 15cm, Width = 8cm

Perimeter = 2L + 2W = 2(15) + 2(8) = 30 + 16 = 46cm Area = L × W = 15 × 8 = 120 cm² Alternative perimeter formula: P = 2(L + W) = 2(15 + 8) = 2(23) = 46cm

Triangle with sides 5cm, 12cm, 13cm and height 12cm to base 5cm

Perimeter = sum of all sides = 5 + 12 + 13 = 30cm Area = ½ × base × height = ½ × 5 × 12 = 30 cm² Note: This is a right triangle (5² + 12² = 13²), so we can use any side as base with corresponding height.

What is circumference and how does it relate to diameter and radius?

Circumference is the perimeter of a circle - the distance around its edge. Formulas: C = 2πr (using radius) C = πd (using diameter) Since diameter = 2 × radius, both formulas are equivalent. Use π ≈ 3.14 for calculations.

Circle with radius 7cm

Circumference = 2πr = 2 × 3.14 × 7 = 43.96cm Area = πr² = 3.14 × 7² = 3.14 × 49 = 153.86 cm² Diameter = 2r = 2 × 7 = 14cm

What is volume and what are its units?

Volume is the amount of three-dimensional space occupied by an object, measured in cubic units (cm³, m³, in³). It represents how much liquid or material can fit inside a 3D shape. Think of it as the capacity of a container.

Cube with edge length 6cm

Volume = a³ = 6³ = 216 cm³ Surface Area = 6a² = 6 × 6² = 6 × 36 = 216 cm² Note: For a cube, all edges are equal length, and there are 6 identical square faces.

Cylinder with radius 4cm and height 10cm

Volume = πr²h = 3.14 × 4² × 10 = 3.14 × 16 × 10 = 502.4 cm³ Think of it as stacking circular discs (area πr²) to height h. Common examples: cans, pipes, water tanks.

Rectangular prism: Length 8m, Width 5m, Height 3m

Volume = L × W × H = 8 × 5 × 3 = 120 m³ This represents the space inside a box-shaped container. Useful for calculating room capacity, storage space, or material needed to fill a rectangular container.

A square field has area 625 m². How much fencing is needed?

Step 1: Find side length from area Area = s² = 625 s = √625 = 25m Step 2: Calculate perimeter Perimeter = 4s = 4 × 25 = 100m Therefore, 100 meters of fencing is needed.

Compare the formulas for area of parallelogram and triangle

Parallelogram: Area = base × height (A = bh) Triangle: Area = ½ × base × height (A = ½bh) Key insight: A triangle has half the area of a parallelogram with the same base and height. This is because you can form a parallelogram by joining two identical triangles.

Trapezoid with parallel sides 8cm and 12cm, height 5cm

Area = ½(b₁ + b₂) × h = ½(8 + 12) × 5 = ½ × 20 × 5 = 50 cm² Formula explanation: Average of parallel sides multiplied by height. Think of it as the area of a rectangle with width equal to the average of the two parallel sides.

Sphere with radius 9cm

Volume = (4/3)πr³ = (4/3) × 3.14 × 9³ = (4/3) × 3.14 × 729 = 3,052.08 cm³ Sphere volume grows very quickly with radius because it's cubed. This formula is used for balls, planets, bubbles, and other spherical objects.

Right circular cone: radius 6cm, height 8cm

Volume = (1/3)πr²h = (1/3) × 3.14 × 6² × 8 = (1/3) × 3.14 × 36 × 8 = 301.44 cm³ Note: Cone volume is 1/3 of a cylinder with same base and height. Examples: ice cream cones, funnels, traffic cones.

A rectangular parking lot is 10m less than twice its width. Perimeter is 400m. Find the length.

Let width = w, then length = 2w - 10 Perimeter = 2L + 2W = 400 2(2w - 10) + 2w = 400 4w - 20 + 2w = 400 6w = 420 w = 70m Length = 2(70) - 10 = 130m

What is the relationship between radius, diameter, and circumference?

Radius (r) = distance from center to edge Diameter (d) = distance across circle through center = 2r Circumference (C) = distance around circle = πd = 2πr Key relationships: d = 2r, C = πd, C = 2πr. If you know any one measurement, you can find the others.

Pyramid with square base 10m × 10m and height 12m

Volume = (1/3) × Base Area × Height Base Area = 10² = 100 m² Volume = (1/3) × 100 × 12 = 400 m³ Pyramid volume is always 1/3 of a prism with the same base and height. Examples: Egyptian pyramids, roof peaks.

A circle has area 78.5 cm². What is its circumference?

Step 1: Find radius from area Area = πr² = 78.5 3.14 × r² = 78.5 r² = 25 r = 5cm Step 2: Calculate circumference C = 2πr = 2 × 3.14 × 5 = 31.4cm