Question

6. The volume of a cuboid is 3240 cm. Its length,
breadth and height are in the ratio 8:5:3. Find
the dimensions of the cuboid.​

Answer 1

Answer:

Step-by-step explanation:

Let the length = 8x

            breadth = 5x

            height = 3x

Volume of a cuboid = length*breadth*height ('*' is multiplied by)

3240 = 8x*5x*3x

3240 = 120x3 (x cubed)

3240/120 = x3

270 = x3

x = 27(cube root)

x = 3

LENGTH = 24CM

BREADTH = 15CM

HEIGHT = 9CM

Answer 2

❥${\underline{\underline{\large{\mathtt{ANSWER:-}}}}}$

Length = 24 cm.

Breadth = 15 cm.

Height = 9 cm.

❥${\underline{\underline{\large{\mathtt{EXPLANATION:-}}}}}$

•Given:-

• Volume of cuboid = 3240 cm³.
• Ratio of length, breadth and height = 8:5:3

•To find:-

• Dimensions of the cuboid.

•Solution:-

Consider,

• Length of the cuboid = 8x cm.
• Breadth of the cuboid = 5x cm.
• Height of the cuboid = 3x cm.

We know,

${\boxed{\sf{\green{Volume\:of\: cuboid\:= Length\times\: Breadth\times\: Height}}}}$

Volume of cuboid= (8x ×5x × 3x)cm³

= 120x³ cm³

According to the question,

$\sf{120x^3\:= 3240}$

$\implies\sf{x^3 = 27}$

$\implies\sf{x\:=3}$

★ Now,find length, breadth, height of the cuboid.

Length = 8 × 3 = 24 cm.

Breadth = 5 × 3 = 15 cm.

Height = 3 × 3 = 9 cm.

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❥${\underline{\underline{\large{\mathtt{VERIFICATION:-}}}}}$

Length = 24 cm.

Breadth = 15 cm.

Height = 9 cm.

Volume = 3240 cm ³.

24×15×9 = 3240

→ 3240 = 3240 (verified)

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