Question

What is the area of a circle 3.102 cmin diameter?

Short answer

The area of the circle is $7.55{\mathrm{cm}}^2$ or $0.0755{\mathrm{m}}^2$.

Step-by-step solution

 Definition of area of circle

The area of a circle is equal to pi (3.14) multiplied by the square of the radius.

 Stating given and known data

Diameter of the circle, $\mathrm{D}=3.102\mathrm{cm}$.

Therefore, radius of the circle, R = 1.551 cm (since R = D/2).

Calculation of area of circle

Write the equation for the area of the circle.

$A={\mathrm{\pi R}}^2$

Substitute $1.551\mathrm{cm}$for R in the above equation.

$$\begin{gathered} \mathrm{A}=3.14\times {\left(1.551\right)}^2 \\ =7.55{\mathrm{cm}}^2 \\ =0.0755{\mathrm{m}}^2 \end{gathered}$$

Conclusion

The area of the circle is $7.55{\mathrm{cm}}^2$ or $0.0755{\mathrm{m}}^2$.