Volume of Cube, Cuboid and Cylinder

9.5 Volume of Cube, Cuboid and Cylinder

Description

Quick Overview

This section explores the concept of volume as the amount of space occupied by three-dimensional objects, focusing on cubes, cuboids, and cylinders.

Standard

In this section, we learn how to calculate the volume of three-dimensional shapes: the cube, cuboid, and cylinder. It includes definitions, measurement methods, and formulas for each shape while emphasizing the transition from two-dimensional area to three-dimensional volume.

Detailed

Volume of Cube, Cuboid and Cylinder

Volume represents the space occupied by three-dimensional objects, measured in cubic units. Unlike area measured in square units, volume involves cubic units to count how many unit cubes fill a solid shape. This section will detail the formulas and measurements required to find the volume of different solids:

Key Shapes Discussed:

  • Cuboid: Defined by its length, breadth, and height. The volume is calculated as \( V = l \times b \times h \), which can also be described as the base area multiplied by the height.
  • Cube: A specific type of cuboid where all sides are equal (l = b = h). Thus, its volume simplifies to \( V = l^3 \).
  • Cylinder: Similar in shape to the cuboid but with circular bases. The volume formula is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) the height.

Understanding these concepts aids in real-world applications, such as packing materials and structural design.

Key Concepts

  • Volume Measurement: Volume is measured in cubic units, representing the space inside a solid object.

  • Cuboid Volume Calculation: The volume of a cuboid is calculated using the formula V = l × b × h.

  • Cube Properties: A cube is a unique cuboid where all its dimensions are equal, and its volume is calculated by V = l³.

  • Cylinder Volume: The volume of a cylinder is determined using V = πr²h, involving the area of its circular base.

Memory Aids

🎵 Rhymes Time

  • If you want to measure space, use cubic units in the right place!

📖 Fascinating Stories

  • Imagine you have a room filled with cubical boxes, all identical. You can fill your room with 27 boxes, so you know your room's volume is 27 cubic meters.

🧠 Other Memory Gems

  • Cubes Create Capacity: Remember that Cubes (C³) shows that volume uses the same measurement for all sides.

🎯 Super Acronyms

CUBES

  • C: for Cuboid
  • U: for Unit
  • B: for Base Area
  • E: for Equal sides (in Cube)
  • S: for Solid shape.

Examples

  • Example 1: A box with dimensions 2 cm × 3 cm × 4 cm has a volume of V = 2 × 3 × 4 = 24 cubic cm.

  • Example 2: A cube with a side length of 5 cm has a volume of V = 5³ = 125 cubic cm.

  • Example 3: A cylinder with radius 3 cm and height 10 cm has a volume of V = π × 3² × 10 ≈ 94.25 cubic cm.

Glossary of Terms

  • Term: Volume

    Definition:

    The amount of space that a three-dimensional object occupies, typically measured in cubic units.

  • Term: Cuboid

    Definition:

    A three-dimensional shape with six rectangular faces, with volume calculated as length × breadth × height.

  • Term: Cube

    Definition:

    A special case of a cuboid where all sides are equal, leading to the formula V = l³ for volume.

  • Term: Cylinder

    Definition:

    A three-dimensional shape with two parallel circular bases, with volume calculated as V = πr²h.