Question

the Length breadth and height of a chocolate boxes are in the ratio 5:4:3 if its volume is 7500 cm cube then find its dimensions​

Answer 1

Answer:

l = 25cm

b = 20 cm

h = 15 cm

Step-by-step explanation:

volume of rectangle= l* b*h

5x * 4x * 3x = 7500

60x³ = 7500

x³ = 7500/60

x³ = 125

x = 5

l = 5*5 = 25

b = 4*5 = 20

h = 3*5 = 15

Answer 2

• The length of a chocolate box = 25 m.
• The breadth of a chocolate box = 20 m.
• The height of a chocolate box = 15 m.

Given :

• The ratio of the length, the breadth and the height of a chocolate box = 5 : 4 : 3.
• The volume of a chocolate box = 7500 cm³.

To Find :

• The dimensions of a chocolate box.

Solution :

Let,

The length of a chocolate box be 5x.

The breadth of a chocolate box be 4x.

The height of a chocolate box be 3x.

First, we need to find the value of x.

Given,

Volume of a chocolate box = 7500 cm³

We know that,

Volume of a chocolate box = length × breadth × height

That means,

length × breadth × height = 7500 cm³

$\rm\implies 5x \times 4x \times 3x = 7500 \: {cm}^{3} \\ \\ \rm \implies 5x \times {12x}^{2} = 7500 {cm}^{3} \\ \\ \rm\implies 60 {x}^{3} = 7500 \: {cm}^{3} \\ \\ \rm\implies {x}^{3} = \frac{750 \cancel0 \: {cm}^{3} }{6 \cancel0} \\ \\ \rm \implies {x}^{3} = \cancel \dfrac{750}{6} \: {cm}^{3} \\ \\ \rm \implies {x}^{3} = \cancel\dfrac{375}{3} \: {cm}^{3} \\ \\ \rm \implies {x}^{3} = 125 \: {cm}^{3} \\ \\ \rm \implies {x}= \sqrt[3]{125 \: {cm}^{3} } \\ \\ \rm \implies x = 5 \: cm$

Hence, the value of x is 5 cm.

So, the dimensions of a chocolate box are :

The length of a chocolate box = 5x = 5 × 5 cm = 25 cm.

The breadth of a chocolate box = 4x = 4 × 5 cm = 20 cm.

The height of a chocolate box = 3x = 3 × 5 cm = 15 cm.

Hence,

The dimensions of a chocolate box are 25 cm, 20 cm and 15 cm.