Each-edge-of-a-parallelepiped-is-1-cm-long-At-one-of-its-vertices-all-three-face-angles-are-acute-and-each-measures-2-Find-the-volume-of-the-parallepiped-Help-me-please-

Question Number 218162 by Ismoiljon_008 last updated on 31/Mar/25

E a c h e d g e o f a p a r a l l e l e p i p e d i s 1 c m l o n g .

A t o n e o f i t s v e r t i c e s, a l l t h r e e f a c e a n g l e s

a r e a c u t e, a n d e a c h m e a s u r e s 2 α .

F i n d t h e v o l u m e o f t h e p a r a l l e p i p e d .

H e l p m e, p l e a s e

Answered by mr W last updated on 31/Mar/25

Commented by mr W last updated on 31/Mar/25

a = b = c = 1

b a s e a r e a A_{B a s e} = a b \sin 2 α = \sin 2 α

h = \sqrt{1^{2} - {(\frac{1 \times \cos 2 α}{\cos α})}^{2}} = \sqrt{1 - \frac{\cos^{2} 2 α}{\cos^{2} α}}

V = A_{B a s e} h = \sin 2 α \sqrt{1 - \frac{\cos^{2} 2 α}{\cos^{2} α}} = 2 \sin^{2} α

Commented by Ismoiljon_008 last updated on 31/Mar/25

T h a n k y o u v e r y m u c h

Commented by Ismoiljon_008 last updated on 31/Mar/25

M r W, w h y i s t h e l e n g t h o f A D e q u a l

t o \frac{1 \cdot c o s 2 α}{c o s α} ?

Commented by mr W last updated on 31/Mar/25

A C = A B \cos 2 α = 1 \times \cos 2 α

A D = \frac{A C}{\cos α} = \frac{1 \times \cos 2 α}{\cos α}

Commented by Ismoiljon_008 last updated on 31/Mar/25

I g o t i t . T h a n k y o u M r W

Commented by mr W last updated on 31/Mar/25

t h e g e n e r a l f o r m u l a :

Commented by mr W last updated on 31/Mar/25

Commented by Ismoiljon_008 last updated on 01/Apr/25

T h a n k s