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Delhi Police Head Constable Prism & Pyramid

Study Material — 2 PYQs (2018–2020) · Concept Notes · Shortcuts

Delhi Police Head Constable Prism & Pyramid is a frequently tested subtopic — 2 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

Delhi Police Head Constable Prism & Pyramid — Past Exam Questions

2 questions from actual Delhi Police Head Constable papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

A rectangular prism has a square base with side length 6 cm and a height of 10 cm. What is the total surface area of the prism?

Exam Q 22020Previous Year Pattern

A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. What is the total surface area of the prism?

Concept Notes

Prism & Pyramid— Rules & Concept

Core ConceptRead this first — the foundation of the topic
CORE CONCEPT

Prism: Imagine a 2D shape (circle, triangle, square) stretched straight up. The top and bottom are identical. All sides are rectangles or parallelograms

Examples

cylinder (circular prism), triangular prism, cube

Pyramid

Imagine a 2D shape as the base, then draw lines from every edge to a single point above. The sides are all triangles

Examples

triangular pyramid (tetrahedron), square pyramid, pentagonal pyramid

KEY RULES FOR PRISM

• Volume = Base Area × Height • Lateral Surface Area = Perimeter of Base × Height • Total Surface Area = 2(Base Area) + Lateral Surface Area • The bases are always parallel and congruent (identical) KEY RULES FOR PYRAMID: • Volume = (1/3) × Base Area × Height • Lateral Surface Area = (1/2) × Perimeter of Base × Slant Height • Total Surface Area = Base Area + Lateral Surface Area • All lateral faces are triangles meeting at apex

Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks

(1) Volume comparisons between prism and pyramid with same base and height. (2) Surface area of square pyramids or triangular prisms. (3) Height/slant height relationships. (4) Word problems combining area and volume

SHORTCUT

For same base and height: Volume of Pyramid = (1/3) × Volume of Prism. This is THE most tested relationship. If a prism has volume 90 cm³, pyramid with same base and height has volume 30 cm³.

Worked ExampleSolve this step-by-step before moving on

A square prism has base side 4 cm and height 10 cm. Find total surface area. Base Area = 4 × 4 = 16 cm² Perimeter of Base = 4 × 4 = 16 cm Lateral Surface Area = 16 × 10 = 160 cm² Total Surface Area = 2(16) + 160 = 32 + 160 = 192 cm²

Exam TrapsCommon mistakes students make — avoid these

Students confuse slant height with perpendicular height in pyramids. Slant height is the distance along the triangular face from base to apex. Perpendicular height is straight down from apex.

Slant height is always longer. Use slant height ONLY for lateral surface area, not volume.

Key Points to Remember

  • Prism: Two identical parallel bases + rectangular sides. Volume = Base Area × Height
  • Pyramid: One base + triangular sides meeting at apex. Volume = (1/3) × Base Area × Height
  • Same base and height: Pyramid volume is always 1/3 of Prism volume (critical exam trick)
  • Lateral Surface Area of Prism = Perimeter × Height; for Pyramid = (1/2) × Perimeter × Slant Height
  • Slant height ≠ perpendicular height in pyramids; slant height is for surface area only
  • Total Surface Area = Base Area(s) + Lateral Surface Area for both shapes

Exam-Specific Tips

  • Volume of prism formula: V = Base Area × Height (where height is perpendicular distance between bases)
  • Volume of pyramid formula: V = (1/3) × Base Area × Height (always one-third of prism with same base and height)
  • Lateral Surface Area of prism: LSA = Perimeter of Base × Height
  • Lateral Surface Area of pyramid: LSA = (1/2) × Perimeter of Base × Slant Height
  • A square pyramid with base side a and slant height l has total surface area = a² + 2al
  • Relationship: If pyramid and prism share same base and height, then Pyramid Volume = (1/3) × Prism Volume
  • A right prism has bases perpendicular to its lateral edges; an oblique prism is slanted
  • A regular pyramid has a regular polygon base with apex directly above the center
Practice MCQs

Prism & Pyramid — Practice Questions

30graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 30

All MCQs →
Practice 1easy

A triangular prism has a triangular base with area 24 cm² and height (length) of the prism is 10 cm. What is the volume of the prism?

Practice 2easy

A triangular pyramid (tetrahedron) has a triangular base with area 36 cm² and height 9 cm. Find its volume.

Practice 3easy

A triangular prism has a triangular base with sides 3 cm, 4 cm, and 5 cm. The height of the prism is 10 cm. What is the lateral surface area of the prism?

Practice 4easy

A rectangular prism has dimensions 5 cm × 6 cm × 10 cm. What is its volume?

Practice 5easy

A pentagonal prism has a pentagonal base with area 50 cm² and the prism's height is 8 cm. What is the volume?

Practice 6easy

A hexagonal pyramid has a hexagonal base with area 54 cm² and height 10 cm. What is the volume of the pyramid?

Practice 7easy

A pentagonal prism has a pentagonal base with area 40 cm² and the prism's length is 7 cm. What is the volume of the prism?

Practice 8easy

A triangular pyramid (tetrahedron) has a triangular base with area 15 cm² and height 12 cm. What is its volume?

Practice 9easy

A triangular pyramid (tetrahedron) has a triangular base with area 24 cm² and a perpendicular height of 9 cm. What is the volume of the pyramid?

Practice 10easy

A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. What is the total surface area of the prism?

Practice 11easy

A rectangular prism has dimensions 8 cm × 6 cm × 4 cm. What is its volume?

Practice 12easy

A rectangular prism has dimensions 6 cm × 4 cm × 5 cm. What is its total surface area?

Practice 13easy

A hexagonal pyramid has a regular hexagonal base with area 72 cm² and height 10 cm. Calculate its volume.

Practice 14easy

A square pyramid has a base side length of 8 cm and height 12 cm. What is the volume of the pyramid?

Practice 15easy

A triangular prism has a triangular base with area 24 cm² and height 15 cm. What is the volume of the prism?

Practice 16easy

A triangular prism has a triangular base with sides 3 cm, 4 cm, and 5 cm. The height of the prism is 10 cm. What is the lateral surface area of the prism?

Practice 17easy

A square pyramid has a base side length of 6 cm and height of 8 cm. What is the volume of the pyramid?

Practice 18medium

A triangular prism has an equilateral triangular base with side 10 cm and prism height 15 cm. What is the lateral surface area of the prism?

Practice 19medium

A rectangular prism has dimensions 5 cm × 8 cm × 10 cm. If the volume is to remain constant, and the length is increased to 16 cm, what should be the new product of width and height?

Practice 20medium

A triangular pyramid (tetrahedron) has an equilateral triangular base with side 6 cm and a height of 4 cm. What is the volume of the pyramid in cm³? (Use √3 ≈ 1.73)

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60-Second Revision — Prism & Pyramid

  • Remember: Pyramid volume = (1/3) × Base Area × Height. Prism volume = Base Area × Height. Pyramid is always 1/3 of prism with same dimensions.
  • Formula: Lateral Surface Area of Prism = Perimeter × Height. For Pyramid = (1/2) × Perimeter × Slant Height.
  • Trap: Don't use perpendicular height for pyramid surface area—always use slant height for lateral area calculations.
  • Total Surface Area = All faces added together. For prism: 2 bases + lateral. For pyramid: 1 base + triangular sides.
  • Quick check: In same-base-height comparison, prism volume ÷ pyramid volume = 3:1 ratio always.
  • Identify the base shape first (triangle, square, pentagon), then apply correct perimeter and area formulas.
  • Slant height can be found using Pythagoras: slant height² = (height)² + (distance from center to base edge)²
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