Area Bounded by a Circle, Surface Area and Volume of Some Solids
Primary 6 · Mathematics
Area Bounded by a Circle, Surface Area and Volume of Some Solids
Lesson 3 of 5
18 min
Let's begin
Mutesi's scout group is sewing a small tent for their camp. The tent is a triangular prism: two triangle ends and three rectangles. How much canvas do they need?
The secret is the same one you used for nets: unfold the solid in your head, find the area of every face, and add them up.
The surface area of a solid is the total area of all its faces. Because a net shows every face exactly once, the surface area is simply the area of the net.
Worked example 1
a box of Rwandan tea, 8 cm × 5 cm × 3 cm.
The rectangles round the sides of a prism can be thought of as one long rectangle wrapped round the base. Its length is the perimeter of the base, and its width is the length (height) of the prism. So:
surface area of a prism = 2 × area of base + perimeter of base × length
Worked example 2
the tent. Each triangular end has a base of 3 m, a height of 2 m, and two sloping sides of 2.5 m. The tent is 4 m long.
The net of a pyramid is its base plus one triangle on each side of the base. The height of each triangular face, measured up its middle, is called the slant height.
Worked example 3
a square-based pyramid with a base of side 6 cm and a slant height of 5 cm.
Tip
Unfold it in your head. List every face, find each area, then add. For a prism, the shortcut is: 2 bases + (perimeter of base × length).
Answers
What you learned today
Sources and credits
The tent story, the tea box and all the worked examples were written by Ganzaa.
Quick check
What is the surface area of a cube with edges of 5 cm?
