How do you find the perimeter or circumference, and the area of a circle with radius 4.2 in?

Jun 13, 2018

See a solution process below:

Explanation:

The formula for the perimeter or circumference of a circle is:

$C = 2 \pi r$

The formula for the area of a circle is:

${A}_{c} = \pi {r}^{2}$

In both formulas $r$ represents the radius of the circle.

Substituting $4.2 \text{ in}$ for $r$ in both formulas gives:

Circumference:

$C = 2 \pi r$ becomes:

$C = 2 \pi \cdot 4.2 \text{ in}$

$C = 8.4 \pi \text{ in}$

If you need a number we can substitute $3.14$ for $\pi$ giving:

$C = 8.4 \cdot 3.14 \text{ in" = 26.376" in}$

Area:

${A}_{c} = \pi {r}^{2}$ becomes:

${A}_{c} = \pi \cdot {\left(4.2 \text{ in}\right)}^{2}$

${A}_{c} = 17.64 \pi {\text{ in}}^{2}$

Again, if you need a number we can substitute $3.14$ for $\pi$ giving:

${A}_{c} = 17.64 \cdot 3.14 {\text{ in"^2 = 55.3896" in}}^{2}$