Question

Karina is designing a logo on a coordinate plane. The logo is a square whose area is 200 square units. She places a circle in the middle of the logo centered at (0,0). The circle passes through the point (6.3,1.6). Approximately what percentage of the logo does the circle cover?
A. 54%
B. 58%
C. 62%
D. 66%

Answer 1

Answer:

D

Step-by-step explanation:

To find the percentage we must first find the area of the circle:

We can find the radius of the circle using the distance formula;

⇒ $d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

⇒ $r = \sqrt{(6.3 - 0)^{2} + (1.6 - 0)^{2}}$

⇒ $r = 6.5$

Now we calculate the area;

⇒ $A = \pi r^{2}$

⇒ $A = \pi (6.5)^{2}$

⇒ $A = \frac{169}{4}\pi$

To get the percentage we divide the area of the circle by the square’s are and multiply by 100;

⇒ $Percentage = \frac{42.25\pi }{200} * 100$

⇒ $Percentage = 66 (2sf)$