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SSC CPO Prism & Pyramid

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This page covers SSC CPO Prism & Pyramid with complete concept notes, 10 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Prism & Pyramid— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

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

2.Exam Patterns

What 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.

3.Worked Example

Solve 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

4.Exam Traps

Common 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

10graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A triangular pyramid (tetrahedron) has a triangular base with area 36 cm² and height 10 cm. What is the volume of the pyramid?

Practice 2easy

A rectangular prism has dimensions 8 cm × 6 cm × 5 cm. What is its total surface area?

Practice 3easy

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

Practice 4easy

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

Practice 5easy

A pyramid with a rectangular base of dimensions 12 cm × 8 cm has a height of 9 cm. What is its volume?

Practice 6medium

A rectangular prism has dimensions 5 cm × 4 cm × 3 cm. A smaller rectangular prism with dimensions 2 cm × 2 cm × 2 cm is removed from one corner. What is the volume of the remaining solid in cm³?

Practice 7medium

A pyramid with a square base of side 10 cm has a height of 12 cm. What is the volume of the pyramid in cm³?

Practice 8medium

A triangular pyramid (tetrahedron) has a triangular base with area 24 cm² and a height of 9 cm. What is the volume of the pyramid in cm³?

Practice 9hard

A rectangular prism has dimensions 8 cm × 6 cm × 4 cm. A pyramid with the same rectangular base (8 cm × 6 cm) and height 12 cm is placed on top of the prism. What is the total volume of the combined solid in cm³?

Practice 10hard

A triangular pyramid (tetrahedron) has an equilateral triangular base with side 10 cm. The height of the pyramid is 12 cm. What is the lateral surface area (excluding the base) in cm²?

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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