Question

the dimension of a cuboid are in the ratio 5 is to 3 is to 2 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

Answer 2

Solutions :-

Let the dimension of the cuboid be 5x, 3x and 2x respectively.

Given : Volume of cuboid = 21870 cm³


A/q

=> 5x × 3x × 2x = 21870
=> 30x³ = 21870
=> x³ = 21870/30
=> x = ³√729 = 9


So,
Length = l = 5 × 9 = 45 cm
Breadth = b = 3 × 9 = 27 cm
Height = h = 2 × 9 = 18 cm


Total surface area of cuboid = 2(lb + bh + hl) square units
= 2(45 × 27 + 27 × 18 × 18 × 45) cm²
= 2 × 2511 cm²
= 5022 cm²


Answer : Total surface area = 5022 cm²