Math Problem Solver

The area of a circle is $\frac{625 \pi}{16} \approx 122.72\, \text{cm}^2$.

Note: Approximate solutions are rounded to the nearest hundredths place.

Given: $$\begin{aligned}d&=\frac{25}{2} = 12.5\end{aligned}$$

Area

The area of a circle is given by the equation: $$\begin{aligned}A&=\pi r^{2}\end{aligned}$$ where $A$ is area and $r$ is radius.

Need:$$\begin{aligned}d&=2 r\end{aligned} \quad \Rightarrow \quad \begin{aligned}\frac{25}{2}&=2 r\end{aligned} \quad \Rightarrow \quad \begin{aligned}r&=\frac{25}{4} = 6.25\end{aligned}$$

Solution:$$\begin{aligned}A&=\pi r^{2}\\A&=\pi \left(\frac{25}{4}\right)^{2}\\A&=\frac{625 \pi}{16}\end{aligned}$$

A circle is a two dimensional figure that has no corners or edges. Its radius r is the distance between the center of the circle and any point on the circle. Its diameter d is twice the radius, forming a line segment passing through the center of the circle.

The circumference C, also known as perimeter P, of a circle is the distance around a circle. $$\begin{aligned} C &= 2 \pi r \\ &= \pi d \end{aligned}$$

The area A of a circle is the region enclosed inside it. $$A = \pi r^{2}$$