Question-40686

Question Number 40686 by MrW3 last updated on 26/Jul/18

Commented by MrW3 last updated on 26/Jul/18

F i n d r a d i u s R o f t h e c i r c u m s p h e r e o f

p y r a m i d .

I g o t R = \frac{\sqrt{3} b^{2}}{2 \sqrt{3 b^{2} - a^{2}}}

Commented by ajfour last updated on 26/Jul/18

Commented by ajfour last updated on 26/Jul/18

R^{2} = x^{2} + \frac{a^{2}}{3} \dots (i)

b^{2} = \frac{a^{2}}{3} + {(R + x)}^{2} \dots . (i i)

f r o m (i i) x = [\frac{\sqrt{3 b^{2} - a^{2}}}{\sqrt{3}} - R]

u s i n g t h i s i n (i)

R^{2} = {[\frac{\sqrt{3 b^{2} - a^{2}}}{\sqrt{3}} - R]}^{2} + \frac{a^{2}}{3}

\Rightarrow \frac{2 R}{\sqrt{3}} (\sqrt{3 b^{2} - a^{2}}) = b^{2}

\Rightarrow R = \frac{b^{2} \sqrt{3}}{2 \sqrt{3 b^{2} - a^{2}}} .

Commented by MrW3 last updated on 26/Jul/18

t h a n k s s i r!

I t r i e d i n t h i s w a y :

h = \sqrt{b^{2} - {(\frac{a}{\sqrt{3}})}^{2}}

\frac{2 R}{b} = \frac{b}{h}

\Rightarrow R = \frac{b^{2}}{2 h} = \frac{b^{2}}{2 \sqrt{b^{2} - \frac{a^{2}}{3}}} = \frac{\sqrt{3} b^{2}}{2 \sqrt{3 b^{2} - a^{2}}}

Commented by ajfour last updated on 26/Jul/18

I t s b e t t e r S i r!

Commented by MrW3 last updated on 26/Jul/18

T h a n k y o u s i r!

I s t h e r e a w a y t o c a l c u l a t e R f o r a n y

p y r a m i d w i t h s i d e s a, b, c (b a s e) a n d

p, q, r ?

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