A square,whose area is s^2 ,contains a semicircle of possible largest area. Determine radius of the semicircle.


Question and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
Question Number 3836 by Rasheed Soomro last updated on 22/Dec/15

$A s q u a r e, w h o s e a r e a i s s^{2}, c o n t a i n s$ $a s e m i c i r c l e o f p o s s i b l e l a r g e s t a r e a .$ $D e t e r m i n e r a d i u s o f t h e s e m i c i r c l e .$
Commented by Yozzii last updated on 24/Dec/15

$r = \frac{s}{2} . I t h i n k t h a t i n o r d e r t o$ $o b t a i n a s e m i - c i r c l e o f l a r g e s t a r e a$ $i n a s q u a r e, i t i s n e c e s s a r y t h a t i t s$ $s t r a i g h t e d g e i s p a r a l l e l t o o n e o f t h e$ $s i d e s o f t h e s q u a r e . I f a n y l a r g e r s i d e l e n g t h$ $i s s o u g h t a f t e r, p a r t o f t h e s e m i c i r c l e$ $l i e s o u t s i d e t h e s q u a r e . I n o t h e r w o r d s,$ $i f t h e a r m r e p r e s e n t i n g t h e s i d e e d g e o f t h e s e m i c i r c l e i s$ $f r e e t o r o t a t e θ ° w i t h i n t h e r e g i o n o f t h e$ $s q u a r e a b o u t o n e o f t h e c o r n e r s o f t h e$ $s q u a r e (θ = a n g l e b e t w e e n a r m a n d s i d e o f s q u a r e), o n l y w h e n θ = 0 ° c a n w e$ $c o m p l e t e l y c o n t a i n a s e m i - c i r c l e i n$ $t h e f i x e d s q u a r e . S o s = 2 r \Rightarrow r = \frac{s}{2} .$
Commented by RasheedSindhi last updated on 24/Dec/15

$S t r a i g h t e d g e o f s e m i c i r c l e i s p a r a l l e l t o o n e$ $o f t h e d i a g o n a l s o f t h e s q u a r e a n d$ $i t t o u c h e s a l l t h e s i d e s o f s q u a r e .$
Commented by RasheedSindhi last updated on 24/Dec/15

$D r a w i n g a s e m i c i r c l e (b y r u l e r$ $a n d c o m p a s s) i n a s q u a r e t h a t$ $t o u c h e s a l l t h e s i d e s o f t h e$ $s q u a r e i s a f a m i l i a r c o n s t r u c t i o n$ $p r o b l e m .$
Commented by Yozzii last updated on 24/Dec/15

$H m m . O k .$
Commented by Rasheed Soomro last updated on 29/Dec/15

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum