Question

the length of a rectangular carton is twice the breadth and thrice the height .if the volume of the carton is 4500cm cube ,find its length ,breadth ,and height .

Answer 1

Solution :

The length of a rectangular carton is twice the breadth and thrice the height.

If the volume of the carton is 4500 cm³, we have to find it's length, breadth and height.

Let us assume that the length of the rectangular carton is x centimetres.

So, the breadth of the carton is x/2 .

And if it's thrice the height of the carton, the height of the carton is x/3 .

Now, the volume of the carton is 4500 cm³

Volume = Length × Breadth × Height

= x . (x/2) . (x/3).

So

x³/6 = 4500

x³ = 4500 × 6

x³ = 27000 = (30)³

Thus, the value of x is 30

The length of the carton is 30 cm

The breadth of the carton is 30/2 = 15 cm

The height of the carton is 30/3 = 10 cm

Answer : The length, breadth and height of the carto. are 30 cm, 15 cm and 10 cm respectively.

Answer 2

Answer:

Given :-

• The length of a rectangular carton is twice the breadth and thrice the height.
• The volume of the carton is 4500 cm³.

To Find :-

• What is the length, breadth and height of a rectangular carton.

Formula Used :-

$\clubsuit$ Volume Of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Volume_{(Rectangle)} =\: Length \times Breadth \times Height}}}\: \: \: \bigstar$

Solution :-

Let,

$\mapsto \bf Length_{(Rectangular\: Carton)} =\: x\: cm$

$\mapsto \bf Breadth_{(Rectangular\: Carton)} =\: \dfrac{x}{2}\: cm$

$\mapsto \bf Height_{(Rectangular\: Carton)} =\: \dfrac{x}{3}\: cm$

According to the question :

$\bigstar$ The volume of the carton is 4500 cm³.

So,

$\footnotesize \implies \bf Volume_{(Rectangle)} =\: Length \times Breadth \times Height$

$\implies \sf 4500 =\: x \times \dfrac{x}{2} \times \dfrac{x}{3}$

$\implies \sf 4500 =\: \dfrac{x \times x \times x}{2 \times 3}$

$\implies \sf 4500 =\: \dfrac{x^3}{6}$

By doing cross multiplication we get,

$\implies \sf x^3 =\: 4500(6)$

$\implies \sf x^3 =\: 4500 \times 6$

$\implies \sf x^3 =\: 27000$

$\implies \sf x =\: \sqrt[3]{27000}$

$\implies \sf\bold{\purple{x =\: 30}}$

Hence, the required length, breadth and height of a rectangular carton is :

$\dag$ Length Of Rectangular Carton :

$\dashrightarrow \sf Length_{(Rectangular\: Carton)} =\: x\: cm$

$\dashrightarrow \sf\bold{\red{Length_{(Rectangular\: Carton)} =\: 30\: cm}}$

$\dag$ Breadth Of Rectangular Carton :

$\dashrightarrow \sf Breadth_{(Rectangular\: Carton)} =\: \dfrac{x}{2}\: cm$

$\dashrightarrow \sf Breadth_{(Rectangular\: Carton)} =\: \dfrac{30}{2}\: cm$

$\dashrightarrow \sf\bold{\red{Breadth_{(Rectangular\: Carton)} =\: 15\: cm}}$

$\dag$ Height Of Rectangular Carton :

$\dashrightarrow \sf Height_{(Rectangular\: Carton)} =\: \dfrac{x}{3}\: cm$

$\dashrightarrow \sf Height_{(Rectangular\: Carton)} =\: \dfrac{30}{3}\: cm$

$\dashrightarrow \sf\bold{\red{Height_{(Rectangular\: Carton)} =\: 10\: cm}}$

$\therefore$ The length, breadth and height of a rectangular carton is 30 cm , 15 cm and 10 cm respectively.

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