A piece of wire is bent into a square that encloses 484 cm². The same wire is then straightened and bent into a circle. What area does the circle enclose? Take $\pi = \frac{22}{7}$ .

154 cm²Correct answerYour answer484 cm²Correct answerYour answer616 cm²Correct answerYour answer2,464 cm²Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The square's side is $\sqrt{484} = 22$ cm, so the wire is $4 \times 22 = 88$ cm long.
The circle's circumference is 88 cm: $2 \times \frac{22}{7} \times r = 88$ , so $r = 14$ cm.
Area = $\frac{22}{7} \times 14 \times 14 = 616$ cm².

Worth noting

The length of wire stays the same, not the area, so 484 cm² is wrong. For the same boundary a circle encloses more area than a square.

Ten questions from Mensuration: Areas and Volumes, at your own pace.

A piece of wire is bent into a square that encloses 484 cm². The same wire is then straightened and bent into a circle. What area does the circle enclose? Take π=227\pi = \frac{22}{7}π=722​.