circles- area of sectors

[rahrah]

B and Z are on circle S. the diameter of circle S is 26, and the measure of angle BSZ = 118 degrees. What is the area of the sector created by arc BZ?
A. 4524.78
B. 118
C. 2262.39
D. 174.03


My Work:
first u have to find the area of the circle :
A= pi(3.14)r(squared)
a= 26(pi)
then find area of the sector:
area of sector= central angle/ 360 (area of circle)

A= 118/360(26pi m squared)
0.338 (26 pi)
26 pi = 81.64
0.338*81.64 = 27.86

None of these are in the answer choice please tell me what it is that i am doing wrong

 

[pka]

B and Z are on circle S. the diameter of circle S is 26, and the measure of angle BSZ = 118 degrees. What is the area of the sector created by arc BZ?
A. 4524.78 B. 118 C. 2262.39 D. 174.03

$\displaystyle \dfrac{118}{360}\cdot 13^2\cdot\pi=~?$

 

[rahrah]

118/360 * 13(squared) * pi =


118/360 * 169 * 3.14
0.338 *169 *3.14
55.39*3.13
174.03 D

thank you so much!!

 

[lookagain]

B and Z are on circle S. the diameter of circle S is 26,
and the measure of angle BSZ = 118 degrees.

What is the area of the sector created by > > arc BZ? < <

* There are two BZ arcs. The minor arc BZ is associated with the angle
of 118 degrees that forms the minor sector BSZ. The major arc BZ is
associated with the reflex angle 242 degrees that forms the major sector BSZ.

* So, despite that the question was involving 118 degrees, it should state,
"What is the area of the sector created by minor arc BZ?"

...

 

[dsk2]

Area of a sector is given by:A=(1/2)*r^2*theta. (A=(1/2)*r*L where L is the length of the sector and L=r*theta. You don't need this formula though, but it is for reference)

This will make life easy for you. Can you remember this formula? A=0.5*r^2*theta. Make sure your theta is in radians. It will give you your answer. Lets try it.

r=13 (right, since diameter=26, makes sense? radius is half of diameter)
theta=118 degrees. ( Now how to convert degrees to radians. Well you know 180 degrees = pi (~=3.14159...you know this pi right). radians. Apparently 1 degree=pi/180 radians). Hence 118 degrees = 118*pi/180 radians.

Thus theta= 118*pi/180 ~= 2.0594 radians.


Now, use the formula.

A=0.5*13^2*2.0594 ~=174.026 square units. (Note that area should always have square units. The same units of radius, but squared.)

Isn't this fun?! Its just one step after you figure out how to change your angle from degrees to radians, and will save you tons of time in your exam!

Oh well, it has already been answered very well.

Cheers,
Sai.

 

[lookagain]

theta = 118 degrees. ( Now how to convert degrees to radians.

Well you know 180 degrees = pi (~=3.14159...you know this pi right). radians.

Apparently 1 degree=pi/180 radians). Hence 118 degrees = 118*pi/180 radians.

Thus theta = 118*pi/180 radians ~= 2.0594 radians.

The word "radians" for the required type of consistent use of units was missing.

 

[JeffM]

Sai, go stand in the corner; 15 minutes!
You'll have company: I think Jeff is still there

I'm always there

 

[sue_riv]

Please help with geometry!!

What is the equation of the circle with center (0, 0) that passes through the point (–6, –6)?
(1 point)

• (x – (–6))² + (y – (–6))² = 72
• x² + y² = 0
• x² + y² = 72
• (x – (–6))² + (y – (–6))² = 0

 

[dsk2]

Agreed lookagain.

sue_riv, may be the question begs for a new thread.

Hint: The equation of a circle with the center at (xc, yc) and having a radius 'r' is:

$\displaystyle (x-x_c)^2+(y-y_c)^2=r^2$


Note: $\displaystyle x_c, r$ and $\displaystyle y_c$ are constants.

 

[lookagain]

What is the equation of the circle with center (0, 0) that passes through the point (–6, –6)?
(1 point)

• (x – (–6))² + (y – (–6))² = 72
• x² + y² = 0
• x² + y² = 72
• (x – (–6))² + (y – (–6))² = 0

sue_riv,

please start your own thread with your question above (or other question) in the "Geometry and Trig" section.