SOLUTION: a circle is inside a square and line from left to right across with a on left side and b on right side--question is if line ab (diameter) is 82cm--what is left not covered by the

Algebra.Com
Question 438554: a circle is inside a square and line from left to right across with a on left side and b on right side--question is if line ab (diameter) is 82cm--what is left not covered by the circle
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


I'll solve the problem in general and then you can apply the solution to your specific case.

If a circle is inscribed in a square, that is the circle is tangent to all 4 sides of the square, then the diameter of the circle and the side of the square are congruent.

Let represent the diameter of the circle.

1. Since the diameter of the circle is congruent with the side of the square, the area of the square is represented by .

2. Since the radius of a circle is half of the diameter, the radius of this circle is . And the area of the circle is then ( times the radius squared)

3. The desired area is the area of the square minus the area of the circle, so:



A little algebra:



And a little calculator work:



Hence, roughly 21.5% of the square remains uncovered. All you need now is the area of your given square and multiply by 0.215]

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism
RELATED QUESTIONS

Four squares with sides 4, 3, 2 and 1 cm are placed side by side left to right, lower... (answered by AnlytcPhil)
Can not figure out how to solve the following. I am to find the value of x and y to... (answered by venugopalramana)
A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point... (answered by rapaljer)
Can someone help me on this problem? I have two parallel lines, I have a line going... (answered by AnlytcPhil)
write a two-column proof. Given: AB ≅ AC Prove: m ⟨B > m ⟨D It's a triangle (answered by mananth)
Given: Triangle ABC with AD bisecting angle BAC, and AE is congruent to ED (both line... (answered by richard1234)
Andre is a butcher and president of a committee, which also includes a grocer, a baker,... (answered by Theo)
Alright, I know only one Question, but I only need you to double check these for me. I... (answered by Alan3354)