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 1 of 5
20 min
Let's begin
Gatete's family has a round cement floor in their yard where they dry beans and sorghum after the harvest. The floor is cracked, and his father wants to resurface it. The shopkeeper asks: "How big is the floor? I need its area to tell you how much cement to buy."
Measuring round the edge is easy with a tape. But how do you find the area of something round, when it has no length and width? That is what this lesson is about.
Take any round thing, a cup, a bicycle wheel or a drum, and divide its circumference by its diameter. You always get the same number, a little more than 3. This number is called π (say "pie"). Its digits go on for ever (3.14159…), so we round it.
In this unit, Ganzaa always uses π = 3.14. Some exam questions say "use π = 227". Whenever a question tells you which value to use, use that one. The value 227 is handy when the radius is a multiple of 7: for a radius of 7 cm, 227 × 7 × 7 = 22 × 7 = 154 cm².
Because C ÷ d = π, the circumference is C = π × d, which is the same as C = 2 × π × r.
Worked example 1
a circle has a radius of 5 cm. C = 2 × 3.14 × 5 = 31.4 cm.
Draw a circle with a radius of 4 cm on 1 cm squared paper. Count the squares that are completely inside, then count the squares that are about half inside as halves. You get close to 50 squares.
Now compare with a square whose side is the radius: 4 × 4 = 16 cm². The circle is a little more than 3 of those squares (3 × 16 = 48). In fact it is exactly π of them: 3.14 × 16 = 50.24 cm².
Cut a paper circle into many equal slices, like a cake. Lay the slices side by side, one pointing up, the next pointing down. The more slices you cut, the more the shape looks like a rectangle:
Area of the rectangle = length × height = π × r × r. So:
area of a circle = π × r × r (also written π r²)
Worked example 2
the drying floor. Its radius is 5 m. A = 3.14 × 5 × 5 = 3.14 × 25 = 78.5 m².
Worked example 3
diameter given. A round flower bed has a diameter of 12 m.
If you forget to halve and use 12 as the radius, you get 3.14 × 144 = 452.16 m², which is four times too big.
Worked example 4
(backwards): a circle has an area of 50.24 cm². Find its radius.
Worked example 5
(a shape made of parts): a garden is a rectangle 10 m by 6 m, with a semicircle on one 6 m end.
Tip
Radius first! If you are given the diameter, halve it before you do anything else.
Then remember which is which: area uses r × r (square units, like m²); circumference uses 2 × r (length units, like m).
Use π = 3.14.
Answers
What you learned today
Sources and credits
The drying-floor story and all the worked examples were written by Ganzaa.
Quick check
Use π = 3.14. A round drum top has a radius of 7 cm. What is its area?
