Question

The length, breadth and height of a cuboid are in the ratio 3 : 5 : 4 and its volume is 7500 cm ^ 3 . Find the length , breadth and height .

Answer 1

ratio = 3:5:4

length = let ratio of 3

= 3x

breadth = let the ratio of 5

= 5y

height= let the ratio of 4

= 4z

from the problem

total volume of the cuboid

volume= ( length ×breadth ×height )

7500cm =( 3x×5x×4x)

7500= 60x

x = 7500/60

x = 125

ratio of 3x=125×3=375

ratio of 5x=125×5=625

ratio of 4x= 125×4=500

therefore : length=375

:breadth =625

:height = 500

Step-by-step explanation:

it may help you

Answer 2

Given:

The length, breadth and the height of a cuboid are in the ratio 3:5:4

The volume of the cuboid is 7500 cm cube.

To find:

The dimension of the cuboid i.e. length, breadth, and the height

So,

Let

• The length of the cuboid be 3x cm
• The breadth of the cuboid be 5x cm
• The height of the cuboid be 4x cm

So,

The formula to find the volume of the cuboid is

$\boxed{\bf{lbh}}$ unit cube.

[In which 'l' is the 'length', 'b'  is the 'breadth' and 'h' is the 'height'.]

So,

⇒ lbh = 7500

⇒ 3x * 5x * 4x = 7500

⇒ 60x³ = 7500

⇒ x³ = 7500 ÷ 60

⇒ x³ = 125

⇒ x = ∛125

⇒ x = 5

So,

The value of the x is 5

Thus,

• The length of the cuboid = 3x = 3*5 = 15 cm
• The breadth of the cuboid = 5x = 5*5 = 25 cm
• The height of the cuboid = 4x = 4*5 = 20 cm

Hence,

Length, breadth, and height of the given cuboid whose sides (length, breadth, and height)ratios are in 3:5:4 and volume is 7500 cm cube, are 15 cm, 25 cm, and 20 cm respectively.