Radius and diameter: the circle mistake that multiplies by four
The question gives the diameter, and your child puts it straight into π × r × r. Because the radius is used twice, the area comes out four times too big. The reverse slip, using the radius for the circumference formula π × d, makes the answer half as big.
What it looks like
A circular table top has a diameter of 1.4 m. Find its area. Take π = 22/7.
- Radius: 1.4 ÷ 2 = 0.7 m
- Area: 22/7 × 0.7 × 0.7 = 1.54 m²
Why 6.16 m² is wrong: The diameter 1.4 m was used as the radius: 22/7 × 1.4 × 1.4 = 6.16 m², four times the real area.
Why children do it
- The question gives one length, and children use whatever number is given without checking what it is.
- Area uses the radius and circumference is easiest with the diameter, so children mix up which goes where.
- The answer is still a sensible-looking decimal, so there is no warning sign.
How to fix it at home
- Ask your child to write "r = ..." on its own line before any circle area calculation.
- Have your child label the given length on a sketch as r or d before choosing a formula.
- Pair the formulas: area uses r × r; circumference uses d (or 2 × r).
- Estimate first: a table 1.4 m across is about the size of a 1.4 m square, so its area must be under 2 m².
Questions parents ask
Should my child use π = 3.14 or 22/7?
Whichever the question says. If the radius is a multiple of 7, 22/7 usually makes the working shorter.
What about semicircles and quarter circles?
The same habit shows up there, plus forgetting to halve or quarter the whole circle. Finding the radius first prevents the first slip.
Where it shows up
Other careless mistakes
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