Question

find the area.
image of a circle with a diameter labeled ( 6w^3 )

Explanation:

Step1: Identify the radius

The diameter of the circle is given as \(6w^3\). The radius \(r\) is half of the diameter, so \(r=\frac{6w^3}{2} = 3w^3\).

Step2: Use the area formula for a circle

The formula for the area \(A\) of a circle is \(A=\pi r^2\). Substitute \(r = 3w^3\) into the formula: \(A=\pi(3w^3)^2\).

Step3: Simplify the expression

First, square \(3w^3\): \((3w^3)^2=3^2\times(w^3)^2 = 9w^6\). Then multiply by \(\pi\): \(A = 9\pi w^6\).

Answer:

The area of the circle is \(9\pi w^6\)