Question

the Length breadth and height of a rectangular solid are in the ratio 5:4:2 if its total area is 1216 cm cube. find the volume of the solid

Answer 1

Answer:

2560 cm³

Step-by-step explanation:

Ratio of Length : Breadth : height = 5 : 4 : 2

Define x:

Let x be the constant ratio

Ratio of Length : Breadth : height = 5x : 4x : 2x

Solve x:

Total surface area = 1216 cm²

2(5x)(4x) + 2(4x)(2x) + 2(2x)(5x) =1216

40x² + 16x² + 20x² = 1216

76x² = 1216

x² = 16

x = √16

x = 4 cm

Find the Dimensions:

Length = 5x = 5(4) = 20 cm

Breadth = 4x = 4(4) = 16 cm

Height = 2x = 2(4) = 8 cm

Find the volume:

Volume = Length x Breadth x Height

Volume = 20 x 16 x 8 = 2560 cm³

Answer: The volume is 2560 cm³