Question

1. express the area in terms of x

circle with diameter 6x

Explanation:

Step1: Find the radius of the circle

The diameter of the circle is \( 6x \), so the radius \( r \) is half of the diameter. That is \( r=\frac{6x}{2}=3x \).

Step2: Use the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A = \pi r^{2} \). Substitute \( r = 3x \) into the formula: \( A=\pi(3x)^{2}=\pi\times9x^{2}=9\pi x^{2} \).

Answer:

The area of the circle in terms of \( x \) is \( 9\pi x^{2} \).