Math Question and Answers


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 48653 by ajfour last updated on 26/Nov/18

Commented by ajfour last updated on 26/Nov/18

$F i n d \frac{r}{R} . S m a l l e r s p h e r e$ $i n s c r i b e d i n s i d e t e t r a h e d r o n$ $a n d l a r g e r o n e c i r c u m s c r i b i n g t h e$ $t e t r a h e d r o n (r e g u l a r) .$
	Answered by mr W last updated on 26/Nov/18

	$l e t a = e d g e l e n g t h$ $\frac{\sqrt{3} a}{2} \times \frac{2}{3} = \frac{\sqrt{3} a}{3}$ $\sqrt{a^{2} - {(\frac{\sqrt{3} a}{3})}^{2}} = \frac{\sqrt{6} a}{3}$ $\frac{2 R}{a} = \frac{a}{\frac{\sqrt{6} a}{3}}$ $\Rightarrow R = \frac{\sqrt{6} a}{4}$ $\frac{\frac{\sqrt{6} a}{3} - r}{r} = \frac{\frac{\sqrt{3} a}{2}}{\frac{\sqrt{3} a}{6}} = 3$ $\Rightarrow r = \frac{\sqrt{6} a}{12}$ $\Rightarrow \frac{r}{R} = \frac{1}{3}$
	Commented by ajfour last updated on 26/Nov/18

	$T h a n k y o u S i r .$ $A n d i f t e t r a h e d r o n i s r e p l a c e d$ $b y a c u b e, t h e n r / R = 1 / \sqrt{3} .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum