Grade 11 Gen Math | Calculate Volume of Three Dimensional (3D) Figures First Term (Term 1) Week 7

Main ideas / lessons

• This video is a Grade 11 General Mathematics (Term 1, Week 7) lesson focused on calculating the volume of 3D (three-dimensional) figures.
• It explains:
  • What volume means: the amount of space occupied by a 3D solid.
  • The common components/variables used in volume formulas, such as height (h), radius (r), and base area (B or base area).
  • How to use volume formulas for different solids and substitute values correctly.
  • How to solve both direct numeric problems and real-life word problems, including composite-style situations (though most examples are single solids).

3D figures reviewed and identified

• Cone
• Sphere
• Cylinder
• Triangular prism
• Cube
• Rectangular prism
• Rectangular pyramid
• Square pyramid

Definition of volume

• Volume = the amount of space occupied by a 3D solid figure.
• Measured in cubic units, such as:
  • cubic cm
  • cubic meter
  • cubic feet

Volume formulas presented (with variable meaning)

Cone

• ( V = \frac{1}{3}\pi r^2 h )
  • ( r ) = radius
  • ( h ) = height

Sphere

• ( V = \frac{4}{3}\pi r^3 )
  • ( r ) = radius

Cylinder

• ( V = \pi r^2 h )
  • ( r ) = radius
  • ( h ) = height

Pyramid (general statement used)

• ( V = \frac{1}{3}(\text{base area})h )
  • base area = area of the pyramid’s base
  • ( h ) = perpendicular height

Cube

• ( V = s^3 )
  • ( s ) = side length

Rectangular prism

• ( V = L \times W \times H )

Triangular prism

• ( V = \frac{1}{2}BH L ) (as stated; interpreted as using triangle base area)
  • ( B ) = base of the triangle
  • ( H ) = height of the triangular base
  • ( L ) = prism length

Method demonstrated for solving problems (step-by-step approach)

• Step 1: Identify the solid type (cone, sphere, cylinder, pyramid, prism, etc.).
• Step 2: Extract the given measurements from the figure:
  • Look for radius, height, and any dimensions needed for base area.
• Step 3: Convert if needed:
  • If the problem gives diameter, convert to radius:
    • ( r = \frac{d}{2} )
• Step 4: Choose the correct volume formula for the solid.
• Step 5: Substitute values carefully.
• Step 6: Simplify exponents/terms first (e.g., compute ( r^2 ), ( r^3 ), and base area before multiplying by height).
• Step 7: Compute the result:
  • Give exact answers using ( \pi ), and/or decimals using ( \pi = 3.14 ).
• Step 8: State correct units:
  • Units are cubic (combine powers when needed).

Examples solved (main results)

Cones

• Example A (cone with radius 2 cm and height 6 cm):
  • Exact: ( 8\pi ) cubic cm
  • Decimal: 25.13 cubic cm
• Another cone (height 10 ft, diameter 8 ft → radius 4 ft):
  • Exact: ( \frac{160\pi}{3} ) cubic feet
  • Decimal: 502.4 cubic feet

Spheres

• Sphere with radius 8 cm:
  • Decimal: 2143.57 cubic cm
• Sphere with diameter 12 ft → radius 6 ft:
  • Decimal: 2712.96 cubic feet

Cylinders

• Cylinder 1: radius 3 cm, height 8 cm
  • Decimal: 226.08 cubic cm
• Cylinder 2: diameter 8 ft → radius 4 ft, height 5 ft
  • Decimal: 251.2 cubic feet

Pyramids

• Square pyramid: side 4 cm, height 10 cm
  • Fraction/decimal described: ( \frac{160}{3} ) cubic cm, 53.33 cubic cm
• Rectangular pyramid: length 6 cm, width 4 cm, height 9 cm
  • Volume: 72 cubic cm

Prisms

• Rectangular prism: ( L=6 ) cm, ( W=4 ) cm, ( H=9 ) cm
  • Volume: 216 cubic cm
• Triangular prism: triangle base 3 cm, triangle height 5 cm, length 10 cm
  • Volume: 75 cubic cm

Real-life application (word problems)

Problem 1: Aquarium

• Dimensions: 60 cm long, 30 cm wide, 40 cm high
• Treated as a rectangular prism
• Volume: 72,000 cubic cm

Problem 2: Ice cream cone

• Radius 3 cm, height 12 cm
• Volume computed for a cone
• Final answers:
  • (36\pi) cubic cm (exact form)
  • 113.04 cubic cm (decimal using ( \pi = 3.14 ))

Formative test (multiple choice) – answers revealed

1. Fish tank volume (rectangular prism): C) 30,000 cubic cm
2. Unit not needed for rectangular prism volume: C) radius
3. Cube side 8 cm: A) 512 cubic cm
4. Triangular prism volume: B) 120 cubic cm
5. Cylinder with ( r=5 ) cm, ( h=8 ) cm (using ( \pi=3.14 )): A) 628 cubic cm

Additional “master the lesson” problems (answers stated)

1. Ball (sphere) ( r=3 ) cm: 113.04 cubic cm
2. Swimming pool ( 10\,m \times 5\,m \times 2\,m ): 100 cubic meters
3. Cube container edge 12 m: 8 cubic meters (note: this appears inconsistent with (12^3), likely a subtitle/auto-generation error)
4. Cylindrical tank ( r=4 ) m, ( h=6 ) m: 301.40… cubic meters (subtitle shows a formatting issue; intended result is about 301.44 cubic meters using ( \pi=3.14 ))
5. Triangular prism base 8 cm, base height 5 cm, length 15 cm: 300 cubic centimeters

Speakers / sources featured

• Native Man tutorial (channel/teacher, presented as “Hello everyone, welcome to Native Man tutorial”)