[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-
- We have given one composite figure which is composed of 2 cuboids
- The dimensions of the large cuboid is 12cm, 10cm and 2cm
- The dimensions of small cuboid is 3cm, 6cm and 8cm
To Find :-
- We have to find the total surface area of the given composite figure .
Let's Begin :-
We have,
- The length, breath and height of the large cuboid is 10cm, 2cm and 12cm
- The length , breath and height of the small cuboid 8cm, 6cm and 3cm
We know that,
Surface area of cuboid
[tex]\bold{\pink{ = 2(lb + bh + hl) }}[/tex]
Therefore,
Surface area of the large cuboid
[tex]\sf{ = 2((10)(2) + (2)(12) + (12)(10)) }[/tex]
[tex]\sf{ = 2( 20 + 24 + 120 ) }[/tex]
[tex]\sf{ = 2( 44 + 120 ) }[/tex]
[tex]\sf{ = 2}{\sf{\times{ 164}}}[/tex]
[tex]\bold{ = 328 cm^{2}}[/tex]
Thus, The surface area of large cuboid is 328 cm²
Now,
Surface area of the small cuboid
[tex]\sf{ = 2((8)(3) + (3)(6) + (6)(8)) }[/tex]
[tex]\sf{ = 2( 24 + 18 + 48 ) }[/tex]
[tex]\sf{ = 2( 42 + 48 ) }[/tex]
[tex]\sf{ = 2}{\sf{\times{ 90}}}[/tex]
[tex]\bold{ = 180 cm^{2}}[/tex]
According to the question,
Total area of composite solid
= Surface area of large cuboid + Surface area of small cuboid - common base area
Subsitute the required values,
[tex]\sf{ = 328 + 180 - ( 6 }{\sf{\times{ 8)}}}[/tex]
[tex]\sf{ = 508 - 48 }[/tex]
[tex]\bold{ = 460 cm^{2}}[/tex]
Hence, The total area of the composite solid is 460 cm² .
