6 ⋅5 Rectangular solid
The region surrounded by three pairs of parallel rectangular planes is known as
rectangular solid.
Let, ABCDEFGH is a rectangular solid, whose length AB a, and breadth
BC b and height AH c
(1) Determining the diagonal: AFis the diagonal of the rectangular solid
ABCDEFGH
In 'ABC,BCAAB and AC is hypotenuse
?AC^2 AB^2 BC^2 a^2 b^2
Again, in 'ACF,FCAAC and AF is hypotenuse
?AF^2 AC^2 CF^2 a^2 b^2 c^2
?AF a^2 b^2 c^2
? the diagonal of the rectangular solid = a^2 b^2 c^2
(2) Determination of area of the whole surface :
There are 6 surfaces of the rectangular solid where
the opposite surfaces are equal figure
Area of the whole surface of the rectangular solid
= 2 (area of the surface of ABCD + area of the
surface of ABGH + area of the surface of
BCFG)
= 2 (ABuADABuAHBCuBG)
= 2 (abacbc)
= 2 (abbcca)
(3) Volume of the rectangular solid = length u width u height
=abc
Example 1. The length, width and height of a rectangular solid are 25 cm., 20 cm.
and 15 cm. respectively. Determine its area of the whole surface, volume and the
length of the diagonal.
Solution : Let, the length of the rectangular solid is a 25 cm., width b 20 cm.
and height c 15 cm.
? Area of the whole surface of the rectangular solid = 2 (abbcca)
= 2 ( 25 u 20 20 u 15 15 u 25 ) sq. cm.
= 2350 square cm.
Volume = abc
= 25 u 20 u 15 cube cm.
= 7500 cube cm.
And the length of its diagonal = a^2 b^2 c^2
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