2.7 Surface Area and Volume of Solids

• Nets of solids
• Surface area of prisms, cylinders, pyramids, cones and spheres
• Volume of prisms, cylinders, pyramids, cones and spheres
• Composite solids
• Applications including capacity and cost

• draw and interpret nets of common solids
• calculate the surface area of prisms, cylinders, cones and spheres
• calculate the volume of prisms, cylinders, pyramids, cones and spheres
• solve problems involving composite solids and capacity
• appreciate the use of volume and surface area in real life

“How much material makes a container, and how much does it hold?”

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1. Surface area
   40 min · 2 practice tasks · quiz
   Unfolding a solid into a net, and adding up the flat pieces.
2. Volume and capacity
   40 min · 2 practice tasks · quiz
   How much a solid holds, and why cones and pyramids get a third.
3. Nets of cubes and cuboids
   40 min · 1 practice tasks · quiz
   A net is a flat pattern that folds into a solid without overlapping faces.
4. Nets of prisms and cylinders
   40 min · 1 practice tasks · quiz
   A prism net is two identical ends plus a row of rectangles; a cylinder net is two circles and one rectangle.
5. Nets of pyramids and cones
   40 min · 1 practice tasks · quiz
   A pyramid net is the base plus triangles; a cone net is a sector whose arc is the base circumference.
6. Surface area of cubes and cuboids
   40 min · 1 practice tasks · quiz
   Paint, wrapping and sheet metal for boxes start from 6s squared or 2(lw + lh + wh).
7. Surface area of prisms
   40 min · 1 practice tasks · quiz
   Total surface area of a prism is two end areas plus the perimeter of the end times the length.
8. Open, closed and hollow cylinders
   40 min · 1 practice tasks · quiz
   Read whether a cylinder has two ends, one end, or a hole down the middle before you add areas.
9. Surface area of pyramids
   40 min · 1 practice tasks · quiz
   A right square pyramid is a square plus four triangles; the face slant comes from the vertical height by Pythagoras.
10. Slant height and surface area of cones
    40 min · 1 practice tasks · quiz
    Find l from r and h, then use pi r l for the curved surface and add pi r squared if the cone is closed.
11. Surface area of spheres and hemispheres
    40 min · 1 practice tasks · quiz
    A sphere is 4 pi r squared; a hemisphere is 2 pi r squared if open and 3 pi r squared if the flat face is included.
12. Volume of prisms
    40 min · 1 practice tasks · quiz
    Any prism has volume equal to the area of its end times its length, including cuboids and triangular prisms.
13. Volume of cylinders and pipes
    40 min · 1 practice tasks · quiz
    A cylinder is a circular prism: pi r squared h. A pipe is the difference of two cylinders.
14. Volume of pyramids, cones and spheres
    40 min · 1 practice tasks · quiz
    Pyramids and cones take one third of the prism or cylinder on the same base; a sphere is four-thirds pi r cubed.
15. Composite solids in Kenyan life
    40 min · 1 practice tasks · quiz
    Split a silo, a tank or an ice-cream into solids you can already do, add or subtract, then convert to litres or shillings.