3.2 Volume of Solids

• Volume of triangular and rectangular-based prisms
• Volume of triangular, rectangular and square-based pyramids
• The volume of a frustum and a sphere

• work out the volume of triangular and rectangular-based prisms
• calculate the volume of a triangular, rectangular and square-based pyramid
• work out the volume of a cone in real-life situations
• determine the volume of a frustum in real-life situations
• calculate the volume of a sphere in real-life situations
• promote the use of volume and capacity of different containers in real-life situations

“How do we determine the volume of different solids?”

“How do we use the volume of solids in real-life situations?”

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1. Volume of a prism: the cross-section carried along
   40 min · 1 practice tasks · quiz
   A prism is one shape repeated along a length, so its volume is the area of that shape times the length.
2. Volume of triangular and rectangular prisms
   40 min · 1 practice tasks · quiz
   Apply the cross-section rule to prisms whose ends are triangles or rectangles.
3. Volume of a pyramid
   40 min · 1 practice tasks · quiz
   A pyramid holds one third of the prism on the same base with the same height.
4. Volume of a cone
   40 min · 1 practice tasks · quiz
   A cone is one third of its cylinder, so its volume is a third of pi r squared h.
5. What a frustum is
   40 min · 1 practice tasks · quiz
   Cut the top off a pyramid or cone parallel to the base and the piece left below is a frustum.
6. Volume of a frustum
   40 min · 1 practice tasks · quiz
   Find the volume of the whole solid, find the small piece removed, and subtract.
7. Volume of a sphere
   40 min · 1 practice tasks · quiz
   A sphere of radius r has volume four thirds pi r cubed, and fills two thirds of its tightest cylinder.
8. Volume and capacity of real containers
   40 min · 1 practice tasks · quiz
   Turn a volume in cubic centimetres into litres, and use it on real Kenyan containers.