Question

1. find the radius of a circle with an area of 380.13 square inches.
2. find the diameter of a circle with an area of $90.25\pi$ square meters.

Explanation:

Step1: Recall circle area formula

The area of a circle is given by $A = \pi r^2$, where $r$ is the radius.

Step2: Solve for radius (Q12)

Rearrange the formula to isolate $r$: $r = \sqrt{\frac{A}{\pi}}$
Substitute $A = 380.13$:
$r = \sqrt{\frac{380.13}{\pi}}$
Use $\pi \approx 3.1416$:
$\frac{380.13}{3.1416} \approx 121$
$r = \sqrt{121} = 11$

Step3: Solve for radius (Q14)

Substitute $A = 90.25\pi$ into $A = \pi r^2$:
$\pi r^2 = 90.25\pi$
Divide both sides by $\pi$: $r^2 = 90.25$
Take square root: $r = \sqrt{90.25} = 9.5$

Step4: Find diameter (Q14)

Diameter $d = 2r$:
$d = 2 \times 9.5 = 19$

Answer:

1. The radius of the circle is 11 inches.
2. The diameter of the circle is 19 meters.