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

D 66%

Explanation:

Answer 2

D

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 = (169)/(4)\pi`

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

⇒
`Percentage = (42.25\pi )/(200) * 100`

⇒
`Percentage = 66 (2sf)`