Question

Circle A has a diameter of approximately 20 inches and an area of approximately 300 in2.

Answer 1

Answer:

4. About 2,700 in2

Step-by-step explanation:

The area of a circle ($A$), measured in square inches, is directly proportional to the square of its diameter ($d$), measured in inches. That is:

$A \propto d^{2}$

$A = k\cdot d^{2}$

Where $k$ is the constant of proportionality, dimensionless.

In consequence, the following relationship between circles A and B is obtained:

$\frac{A_{B}}{A_{A}} = \frac{d_{B}^{2}}{d_{A}^{2}}$

The area of the circle B is now cleared:

$A_{B} =\left(\frac{d_{B}}{d_{A}} \right)^{2}\cdot A_{A}$

Given that $d_{A} = 20\,in$, $d_{B} = 60\,in$ and $A_{A} = 300\,in^{2}$, then:

$A_{B} = \left(\frac{60\,in}{20\,in} \right)^{2}\cdot (300\,in^{2})$

$A_{B} = 2700\,in^{2}$

Therefore, the correct answer is 4.