Circle Area & Circumference - Pre Algebra

1. What is the exact circumference of a circle with diameter 10 in?

   $10\pi$ inches, since $C = \pi d$.

2. Using $\pi \approx 3.14$, what is the area of a circle with radius 3 m?

   28.26 square meters, since $3.14 \times 9 = 28.26$.

3. What is the formula for the circumference of a circle?

   $C = 2\pi r$, or equivalently $C = \pi d$, since the diameter is twice the radius.

4. If the radius of a circle is doubled, by what factor does its area change?

   It is multiplied by 4, since $\pi(2r)^2 = 4\pi r^2$.

5. A circle has area $49\pi$ square meters. What is its diameter?

   14 meters. From $\pi r^2 = 49\pi$, $r = 7$, so $d = 14$.

6. A circular track has inner radius 40 m and outer radius 45 m. What is the exact area of the track between the circles?

   $425\pi$ square meters, since $\pi(45^2 - 40^2) = \pi(2025 - 1600) = 425\pi$.

7. What is the exact area of a semicircle with radius 4 cm?

   $8\pi$ square centimeters, half of the full circle's $16\pi$.

8. What ratio in every circle equals $\pi$?

   Circumference divided by diameter, $\frac{C}{d}$, which is about 3.14.

9. What is the formula for the area of a circle?

   $A = \pi r^2$, where $r$ is the radius.

10. A circle has circumference $24\pi$ ft. What is its radius?

    12 feet. From $2\pi r = 24\pi$, $r = 12$.

11. What is the exact area of a circle with radius 5 cm?

    $25\pi$ square centimeters, since $\pi(5)^2 = 25\pi$.

12. What kind of units does circumference use, and what kind does area use?

    Circumference is a length, in linear units such as cm. Area uses square units such as square centimeters.

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