Circles: Practice

A segment from the center out to the edge is the radius. The diameter crosses the whole circle through the center, a chord joins two edge points, and the circumference is the distance around the boundary.

Since $\pi = \dfrac{C}{d}$, multiplying both sides by $d$ gives the circumference.

$C = \pi d$

The form $\pi r^2$ is the area, not the circumference.

Use $C = \pi d$ with the diameter given.

$C = 3.14 \times 5 = 15.7 \text{ cm}$

Every chord joins two points on the circle. The longest one possible is the chord that passes through the center, and that special chord is the diameter. (An arc is curved, so it is not a chord at all.)

The area of a circle is

$A = \pi r^2,$

which squares the radius. The expression $2\pi r$ is the circumference, a length, not an area.

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

$r^2 = 3^2 = 9$

Then multiply by $\pi$:

$A = 3.14 \times 9 = 28.26 \text{ cm}^2$

The diameter is twice the radius.

$d = 2r = 2 \times 9 = 18 \text{ in}$

The distance around a circle is its circumference, the circle's version of a perimeter. The radius and diameter are straight segments, not the distance around.

Because $d = 2r$, substitute into $C = \pi d$.

$C = \pi d = \pi (2r) = 2 \pi r$

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

$r^2 = 2^2 = 4$

Then multiply by $\pi$:

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

A diameter is two radii laid end to end through the center, so it is twice as long as the radius.

$d = 2r$

Use $C = 2\pi r$ with the radius given.

$C = 2 \times 3.14 \times 1 = 6.28 \text{ cm}$