Question

the edges of cuboid are in ratio of 1:2:3 and volume is 1296 cm² find length breadth and heigh​

Answer 1

Answer:

Length, breath, height of the cuboid is 18cm, 12cm and 6cm respectively.

Given:

• Ratio of edges of a cuboid = 1 : 2 : 3
• Volume of the cuboid = 1296 cm³

To Find:

• Length, Breath and height of the cuboid.

Solution:

Let the height of the cuboid = x

Let the breath of the cuboid = 2x

Let the length of the cuboid = 3x

Volume of the cuboid = length × Breath × height

⟾ 1296 cm³ = ( x × 2x × 3x )

⟾ 1296 cm³ = 6x³

⟾ 1296 cm³ / 6 = x³

⟾ 216 cm³ = x³

⟾ ³√216cm³= x

⟾ 6cm = x

Height = x = 6cm

Breath = 2x = 2(6cm) = 12cm

Length = 3x = 3(6cm) = 18cm

Answer 2

Question ::-

The edges of cuboid are in ratio of 1:2:3 and volume is 1296 cm² find length breadth and height ?

Given ::-

• Ratio of length, height , cuboid = 1:2:3

• Volume = 1296 ${cm}^{3}$

To find ::-

• Length , breadth , height ?

Formula used ::-

$volume \:= \: length \times breadth \times height$

Solution ::-

let the common factor be x

• Height = x
• Breadth = 2x
• Length = 3x

__________

$⟼ \: \: \: \: 1296 {cm}^{3} = (x \times 2x \times 3x)$

$⟼ \: \: \: \: 1296 {cm}^{3} = \: 6 {x}^{3}$

$⟼ \: \: \: \: \dfrac{1296}{6} {cm}^{3} = \: {x}^{3}$

$⟼ \: \: \: \: 216 {cm}^{3} = \: {x}^{3}$

$⟼ \: \: \: \: \sqrt[3]{216} {cm}^{3} = \: x$

$⟼ \: \: \: \: x = 6cm$

__________

• Height = x = 6cm

• Breadth = 2x = 2×6 = 12cm

• Length = 3x = 3×6 = 18 cm