Circles: Practice

A semicircle is half a full circle, so its area is half of $\pi r^2$.

$A = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 6^2 = \frac{1}{2} \times 113.04 = 56.52 \text{ cm}^2$

The diameter is given, so use $C = \pi d$ directly.

$C = 3.14 \times 2 = 6.28 \text{ m}$

Circumference uses $2\pi r$ and is a length:

$C = 2 \times 3.14 \times 5 = 31.4 \text{ m}$

Area uses $\pi r^2$ and is in square units:

$A = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ m}^2$

Starting from $C = \pi d$, divide the circumference by $\pi$ to recover the diameter.

$d = \frac{C}{\pi} = \frac{31.4}{3.14} = 10 \text{ cm}$

The true value of $\pi$ is about $3.14159\ldots$, with digits that never stop and never settle into a repeating pattern. We round it to $3.14$ for computation, so any result built from it is approximate. (The fraction $\tfrac{22}{7}$ is also only close, not exact.)

The diameter is given, so use $C = \pi d$.

$C = 3.14 \times 18 = 56.52 \text{ m}$

The ratio of circumference to diameter is $\pi$ for every circle, because scaling a circle multiplies its circumference and its diameter by the same factor, which cancels in the ratio.

$\frac{C}{d} = \pi$

So both circles share the same ratio, $\pi$, no matter their sizes.

Use $A = \pi r^2$. Square the radius first.

$r^2 = 1.5^2 = 2.25$

$A = 3.14 \times 2.25 = 7.065 \text{ m}^2$

The curved edge of a semicircle is half the full circumference.

$\text{curve} = \frac{1}{2}(2\pi r) = \pi r = 3.14 \times 10 = 31.4 \text{ cm}$

(The full perimeter of the semicircle would also add the straight diameter, but here only the curved part is asked for.)

Area counts how many unit squares fit inside a region, so it is reported in square units like $\text{cm}^2$. Circumference, diameter, and radius are all lengths, measured in linear units.

Halve the diameter to get the radius, then use $A = \pi r^2$.

$r = \frac{4}{2} = 2 \text{ cm}$

$A = 3.14 \times 2^2 = 3.14 \times 4 = 12.56 \text{ cm}^2$

Use $A = \pi r^2$ with the rough value $\pi \approx 3$ to estimate.

$A \approx 3 \times 10^2 = 3 \times 100 = 300 \text{ cm}^2$

The exact value with $\pi \approx 3.14$ is $314 \text{ cm}^2$, close to the estimate.