CBSE Class 9 Answered

Respected sir/madam,

You have mentioned the length of diagonal of a cube =

Can you explain everything about this formula with the help of a diagram?

Asked by Varsneya Srinivas | 07 Feb, 2015, 09:20: AM

Expert Answer

Consider the following diagram.

T h e space a b o v e space f i g u r e space i s space a space c u b e comma space w i t h space a space m e t r e s. S i n c e space i t space i s space a space c u b e comma space a l l space o f space i t s space s i d e s space a r e space s q u a r e s. T h u s comma space t h e space c o r n e r space a n g l e space i s space a l w a y s space 90 degree space a n d space h e n c e space w e space c a n space a p p l y space P y t h a g o r a s space T h e o r e m. L e t space A C space b e space t h e space d i a g o n a l space o f space t h e space s q u a r e space A B C D space a n d space i t space d i v i d e s space t h e space s q u a r e space i n t o space t w o space t r i a n g l e s o f space e q u a l space a r e a s. N o w space c o n s i d e r space t h e space r i g h t space t r i a n g l e space A B C colon A p p l y i n g space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma A B squared plus B C squared equals A C squared rightwards double arrow a squared plus a squared equals A C squared rightwards double arrow 2 a squared equals A C squared rightwards double arrow A C equals a square root of 2 D r a w space a space l i n e space f r o m space A space t o space G. F r o m space t h e space d i a g r a m space i t space i s space c l e a r space t h a t space A G space i s space t h e space d i a g o n a l space o f space t h e space c u b e. C o n s i d e r space t h e space r i g h t space t r i a n g l e space A G C colon A g a i n space a p p l y i n g space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma A C squared plus G C squared equals A G squared rightwards double arrow open parentheses 2 a squared close parentheses plus a squared equals A G squared rightwards double arrow 3 a squared equals A G squared rightwards double arrow A G equals a square root of 3 space m

Answered by Vimala Ramamurthy | 07 Feb, 2015, 09:52: AM

CBSE Class 9 Answered

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CBSE Class 9 Answered

Application Videos

Surface Area of Cube and Cuboid

Concept Videos

Surface Area of a Cube and Cuboid ...

Surface Area of a Cube and Cuboid

Surface Area of a Cube and Cuboid

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