A learner finds the area of a circle whose diameter is 12 centimetres, taking π as exactly 3.14, and writes: the area is 3.14 times 12 times 12, which is 452.16 square centimetres. Which statement names the mistake in this circle-measures working and gives the correct area?
The working is correct, since the length multiplied by itself in the area rule is always the longest measurement across the circle.
The area rule multiplies by the width just once, so the area is 37.68 square centimetres.
The 12 centimetres is the full width, so the half-width 6 is what must be squared, giving 113.04 square centimetres.✓Respuesta correcta
The learner should simply halve the result, giving 226.08 square centimetres.
Explicación
The rule for the space inside a circle squares the distance from the centre to the curve, and that distance is 6 when the full width is 12. Feeding the whole width into the rule squares a length twice as long, which multiplies the result by four rather than nudging it slightly upward.