Question

circle A has a diameter of approimately 300 in 2 . circle B has a diameter of approximately 60 inches . which of these could be the area of circle B

Answer 1

2700in^2

Step-by-step explanation:

From the question, we've been given the below parameters;

`\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}`

Since Area of a circle is always directly proportional to the square of the diameter, so we'll have;

`\begin{gathered} A\alpha d^2 \\ A=k\ast d^2 \\ k=(A)/(d^2) \end{gathered}`

wh

So we can express the relationship between circle A and B as follows;

`\begin{gathered} (A_A)/(A_B)=(d^2_A)/(d^2_B)_{}_{}^{_{}}_{} \\ \therefore A_B=((d^2_B)/(d^2_A))\ast A_A \\ =((60)/(20))^2\ast300 \\ =(3600)/(400)\ast300 \\ =2700in^2 \end{gathered}`