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

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Answer 1 · 2018-06-13T12:06:05

See a solution process below:

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

$C = 2 π r$ $C= 2pir$

The formula for the area of a circle is:

$A_{c} = π r^{2}$ $A_c = pir^2$

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

Substituting $4.2 in$ $4.2" in"$ for $r$ $r$ in both formulas gives:

Circumference:

$C = 2 π r$ $C= 2pir$ becomes:

$C = 2 π \cdot 4.2 in$ $C= 2pi * 4.2" in"$

$C = 8.4 π in$ $C= 8.4pi" in"$

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

$C = 8.4 \cdot 3.14 in = 26.376 in$ $C = 8.4 * 3.14" in" = 26.376" in"$

Area:

$A_{c} = π r^{2}$ $A_c = pir^2$ becomes:

$A_{c} = π \cdot {(4.2 in)}^{2}$ $A_c = pi * (4.2" in")^2$

$A_{c} = 17.64 π {in}^{2}$ $A_c = 17.64pi" in"^2$

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

$A_{c} = 17.64 \cdot 3.14 {in}^{2} = 55.3896 {in}^{2}$ $A_c = 17.64 * 3.14" in"^2 = 55.3896" in"^2$