Question

the dimensions of the cuboid are in the ration 7:5:3 if its volume is 6720 cm find its dimensions

Answer 1

Step-by-step explanation:

ratio of sides is 7:5:3

sides be 7y , 5y and 3y

volume of cuboid = 6720 cubic cm

lbh=6720

7y X 5y X 3y X=6720

$105 {y}^{3} = 6720$

${y}^{3} = 6720 \div 105$

${y}^{3} = 64$

$y = \sqrt[3]{64}$

$y = 4$

so sides be

7y=28cm

5y=20cm

3y=12cm

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Answer 2

Given

• Ratio of the dimensions of the cuboid = 7 : 5 : 3
• Volume of the cuboid = 6720 cm³

To find

• Dimensions of the cuboid

Solution

Let the dimensions of the cuboid be -:

• Length of the cuboid = 7x
• Breadth of the cuboid = 5x
• Height of the cuboid = 3x

Using formula,

Volume of the cuboid = lbh

where,

• l = length of the cuboid
• b = breadth of the cuboid
• h = height of the cuboid

Substituting the values,

⟶ 6720 = 7x × 5x × 3x

⟶ 6720 = 105x³

⟶ 6720/105 = x³

⟶ 64 = x³

⟶ ∛64 = x

⟶ ± 4 Reject - ve = x

⟶ x = 4

The value of x = 4

Therefore, The dimensions of the cuboid :-

• Length of the cuboid = 7x = 7 × 4 = 28 cm
• Breadth of the cuboid = 5x = 5 × 4 = 20 cm
• Height of the cuboid = 3x = 3 × 4 = 12 cm