Area of a Circle – Exact Answer (d = 10 cm)

\(25\pi\) cm²

Explanation

Since the length of the diameter is 10 centimeters and the length of a diameter is twice the length of a radius, the length of the radius is 5 centimeters.

\[A = \pi r^2\]

This is the formula for the area of a circle.

\[A = \pi (5)^2\]

Substitute 5 for \(r\), the radius of the circle. The notation \(\pi r^2\) means \(\pi \times r^2\).

\[= \pi(25)\]

Evaluate the exponential expression: \(5^2 = 25\).

\[= 25\pi\]

Write the product so that \(\pi\) is the last factor.

The exact area of the circle is \(25\pi\) cm².