Question

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

Answer 1

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

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

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

❥ The length of a chocolate box = 25 m.

❥ The breadth of a chocolate box = 20 m.

❥ The height of a chocolate box = 15 m.

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

❥ The ratio of the length, the breadth and the height = 5 : 4 : 3.

❥ The volume of a chocolate box = 7500 cm³.

$\Large{\underline{\underline{\bf{FiNd:-}}}}$

What are the dimensions of a chocolate box ?

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Here we go !

Considering

↠length be 5x.

↠ The breadth be 4x.

↠ The height be 3x.

We know that,

↠ Volume of cuboid = lbh

Let's find out the value of x

Now , According to the Given

length × breadth × height = 7500 cm³

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

Therefore ,

$\red{\bigstar}$ The value of x

$\huge\leadsto{\sf\purple{5\: cm}}$

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.

$\therefore\underline{\boxed{\textsf{The Length is = {\textbf{25}}}}} \qquad\qquad \bigg\lgroup\bold{ \ Answer}\bigg\rgroup$

$\underline{\boxed{\textsf{The breadth is = {\textbf{20}}}}} \qquad\qquad \bigg\lgroup\bold{\ Answer}\bigg\rgroup$

$\underline{\boxed{\textsf{The Height is = {\textbf{15}}}}} \qquad\qquad \bigg\lgroup\bold{\ Answer}\bigg\rgroup$

Answer 2

Given :-

Ratio = 5:4:3

Volume = 7500 cm³

To Find :-

The dimensions

Solution :-

Let the length, breadth and height be 5x, 4x, and 3x respectively.

We know that,

Volume of cuboid = l × b × h

= 5x × 4x × 3x

= 60x³

But also given that,

Volume = 7500 cm³

A/q,

7500 cm³ = 60x³

$\implies\: x^3\: =\: {\dfrac{7500}{60}}$

=> x³ = 125

$\implies\: x\: =\: {\sqrt[3]{125}}$

$\implies\: x\: =\: 5$

Now,

Length = 5x = 5×5 = 25 cm

Breadth = 4x = 4×5 = 20 cm

Height = 3x = 3×5 = 15 cm