Answer:
2700in^2
Explanation:
From the question, we've been given the below parameters;
[tex]\begin{gathered} \text{Area of circle A(A}_A)=300in^2 \\ \text{Diameter of circle A (d}_A)=20in \\ AreaofcircleB(A_B)=\text{ to be }\det er\min ed \\ \text{Diameter of Circle B (A}_B)=60in \end{gathered}[/tex]
Since Area of a circle is always directly proportional to the square of the diameter, so we'll have;
[tex]\begin{gathered} A\alpha d^2 \\ A=k\ast d^2 \\ k=\frac{A}{d^2} \end{gathered}[/tex]
wh
So we can express the relationship between circle A and B as follows;
[tex]\begin{gathered} \frac{A_A}{A_B}=\frac{d^2_A}{d^2_B}_{}_{}^{_{}}_{} \\ \therefore A_B=(\frac{d^2_B}{d^2_A})\ast A_A \\ =(\frac{60}{20})^2\ast300 \\ =\frac{3600}{400}\ast300 \\ =2700in^2 \end{gathered}[/tex]
