
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 6th, 2015, 10:19 AM  #1 
Newbie Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0  Calculating the radius & angle of sector.
Hi All, wondering if anyone is able to help me solve this problem; Length of an arc of a circle is 6cm. The corresponding sector area is 150cm squared. Calculate i) the radius of the circle and ii) the angle subtended at the centre of the circle by the arc I found the radius by setting up a pair of simultaneous equations using arc length =r*theta and area of sector= 1/2*r^2*theta. By using these I calculated the radius to be 50cm which surely cannot be correct? Any help would be great thanks!! Last edited by wahhdoe; December 6th, 2015 at 10:37 AM. 
December 6th, 2015, 12:40 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,947 Thanks: 1555 
$s = r \cdot \theta \implies \theta = \dfrac{s}{r}$ $A = \dfrac{1}{2}r^2 \theta$ $A = \dfrac{1}{2}r^2 \cdot \dfrac{s}{r}$ $A = \dfrac{1}{2}r \cdot s$ $r = \dfrac{2A}{s} = \dfrac{300}{6} = 50 \text{ cm}$ $\theta = \dfrac{6}{50} = \dfrac{3}{25} \text{ radians } \approx 7^\circ$ 
December 6th, 2015, 06:52 PM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 
Let me try : $\displaystyle \frac{6}{150}=\frac{2\cancel{\pi}r}{\cancel{\pi}r^ 2}$ $\displaystyle \frac{1}{25}=\frac{2r}{r^2}$ $\displaystyle \frac{1}{25}=\frac{2}{r}$ $\displaystyle r=2\times25$ r = 50 $\displaystyle \frac{\theta}{360^o}=\frac{6}{2\pi\times50}$ $\displaystyle \frac{\theta}{360^o}=\frac{6}{100\pi}$ $\displaystyle \frac{\theta}{2\cancel{\pi}}=\frac{3}{50 \cancel{\pi}}$ $\displaystyle \theta=\frac{3\times2}{50}$ $\displaystyle \theta=\frac{6}{50}$ $\displaystyle \theta=\frac{3}{25}$ 

Tags 
angle, calculating, radius, sector 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculating Circle Center Point With radius  joelphilippage  Geometry  3  September 17th, 2014 03:53 PM 
Calculating angle sin and sin angle without any functions.  Gyiove  Algebra  1  February 26th, 2014 04:57 PM 
Calculating radius to x and y point  xninjaxelitex  Algebra  1  June 5th, 2013 12:29 AM 
Calculating circle's coordinates using radius and rotation?  Mercury  Algebra  6  February 19th, 2013 08:58 PM 
Calculating radius to x and y point  xninjaxelitex  Computer Science  0  December 31st, 1969 04:00 PM 