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4 votes
4 votes
Is the area of a square with side length 2 inches greater than or less than the area of a circle with radius 1.2 inches?

User Predrag
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1 Answer

24 votes
24 votes

Answer:

less

Explanation:

We can answer the question about relative sizes of a square and a circle by finding the area of each.

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The area of the square is ...

A = s²

A = (2 in)² = 4 in²

The area of the circle is ...

A = πr²

A = π(1.2 in)² = 1.44π in² ≈ 4.524 in²

The area of the square is less than the area of the circle.

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Additional comment

The area of a circle is π/4 times the area of the square in which it is inscribed. If the diameter of the circle is 1.2 times the side length of the square, its area ratio to the square will be (1.2²)(π/4) = 0.36π ≈ 1.13. That is, the circle is larger and the square is smaller.

User Prtdomingo
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