Question

a circular disc has an area that measures between 1,650 and 1,700 square inches.

what could be the length of its radius? use 3.14 for \\(\pi\\).

23 in.
24 in.
25 in.
26 in.

Explanation:

Set up the inequality for the area of the circle

$$ 1650 < \pi r^2 < 1700 $$

$$ 1650 < 3.14 \cdot r^2 < 1700 $$

Solve for the range of the radius

$$ \frac{1650}{3.14} < r^2 < \frac{1700}{3.14} $$

$$ 525.48 < r^2 < 541.40 $$

$$ \sqrt{525.48} < r < \sqrt{541.40} $$

$$ 22.92 < r < 23.27 $$

Evaluate the given options

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Answer:

• (A) 23 in. (Correct answer)
• (B) 24 in.
• (C) 25 in.
• (D) 26 in.