The dimension of a cuboid are in the ratio 5 ratio 3 ratio to its volume is 21870 cm cube find its total surface area
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Given :
The dimension of a cuboid are in the ratio 5 : 3 : 2
Volume of cuboid = 21870 cm³
Let the length, breadth and height of the cuboid be 5x, 3x and 2x respectively.
According to the question,
Volume of cuboid = lbh cubic units
=> 21870 = 5x × 3x × 2x
=> 21870 = 30x³
=> 21870/30 = x³
=> 729 = x³
=> √(9 × 9 × 9) = x = 9
Therefore,
Length = 5x = 5 × 9 = 45 cm
Breadth = 3x = 3 × 9 = 27 cm
Height = 2x = 2 × 9 = 18 cm
Find the total surface area of cuboid :-
Total surface area of cuboid
= 2(lb + bh + hl) sq. units
= 2 (45 × 27 + 27 × 18 + 18 × 45) cm²
= 2 (1215 + 486 + 810) cm²
= 2 × 2511 cm²
= 5022 cm²
Hence,
Total surface area of cuboid = 5022 cm²
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