SOLUTION: 1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree. ----------- ----------- ---- 2. Solve the pro

Algebra ->  Pythagorean-theorem -> SOLUTION: 1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree. ----------- ----------- ---- 2. Solve the pro      Log On


   



Question 319945: 1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.
----------------------------
2. Solve the proportion:
h%22%3A%2210%22=%221%22%3A%22sqrt%282%29
Show that the answer is h%22=%225sqrt%282%29

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The Question:find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.
h:10=1:root 2
---
Equation:
h/10 = 1/sqrt(2)
---
h = 10/sqrt(2)
---
h = 10sqrt(2)/2
---
h = (10/2)sqrt(2)
---
h=5 root 2
My Question: how do you get 1 after the equal sign?
---
The "1" is the numerator of the right side of the equation.
=============================================
Cheers,
Stan H.
=============================================

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.

That's the red area below:


The area of the sector A is to 45° as the area of the whole circle is to 360°:

The area of a whole circle is 

A=pi%2Ar%5E2pi%2A10%5E2%22=%22100pi

So

A%22%3A%22%2245%22%22=%22100pi%22%3A%22360

A%2F45%22=%22%28100pi%29%2F360

Cross-multiply:

360A=4500pi

Divide both sides by 360

%28360A%29%2F360=%284500pi%29%2F360

A=%284500pi%29%2F360

A=25pi%2F2

-------------------------------

2. Solve the proportion:

h%22%3A%2210%22=%221%22%3A%22sqrt%282%29

h%2F10%22=%221%2Fsqrt%282%29

Cross-multiply:

sqrt%282%29%2Ah%22=%2210%2A1

sqrt%282%29%2Ah%22=%2210

Divide both sides by sqrt%282%29

%28sqrt%282%29%2Ah%29%2Fsqrt%282%29%22=%2210%2Fsqrt%282%29

Cancel on the left:

%28cross%28sqrt%282%29%29%2Ah%29%2Fcross%28sqrt%282%29%29%22=%2210%2Fsqrt%282%29

h%22=%2210%2Fsqrt%282%29

Rationalize the denominator on the right side by multiplying it by sqrt%282%29%2Fsqrt%282%29

h%22=%2210%2Fsqrt%282%29%22%D7%22sqrt%282%29%2Fsqrt%282%29

h%22=%22%2810sqrt%282%29%29%2F2

h%22=%225sqrt%282%29

Edwin