Perimeter of a sector

Geometry Level 3

The sector of this circle has a perimeter of 36cm. Find the area. (Where the 2 line segments meet is the centre of the circle) Give an exact answer. Note that all the answers are in cm².

(5184π)/(16+24π+9π²) 136.366 67.774 (458π)/(46+68π-6π²) (3888π)/(16+24π+9π²) 90.365

Anthony Wilson by Anthony Wilson , 17, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Zico Quintina
May 23, 2018

Let r r be the radius of the circle (sector) in cm. Then

Perimeter = 3 4 ( 2 π r ) + 2 r = 36 r ( 3 π + 4 ) = 72 r 2 ( 9 π 2 + 24 π + 16 ) = 5884 3 4 π r 2 ( 9 π 2 + 24 π + 16 ) = 3888 π Area = 3 4 π r 2 = 3888 π ( 9 π 2 + 24 π + 16 ) \begin{aligned} \text{Perimeter }= \dfrac{3}{4} (2 \pi r) + 2r &= 36 \\ \\ r (3 \pi + 4) &= 72 \\ \\ r^2 (9 \pi^2 + 24 \pi + 16) &= 5884 \\ \\ \dfrac{3}{4} \pi r^2 (9 \pi^2 + 24 \pi + 16) &= 3888 \pi \\ \\ \text{Area } = \dfrac{3}{4} \pi r^2 &= \boxed{ \dfrac{3888 \pi}{(9 \pi^2 + 24 \pi + 16)} } \end{aligned}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...