Question

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

Answer 1

Solutions :-

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