Question

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​

Answer 1

GIVEN :-

• Length, breadth and height of a chocolate box are in the ratio 5 : 4 : 3

• Volume of the chocolate box = 7500 cm³

TO FIND :-

• The dimensions of chocolate box.

SOLUTION :-

Let,

Length of the chocolate box = 5x

Breadth of the chocolate box = 4x

Height of the chocolate box = 3x

We know that,

Volume of cuboid = lbh

$\longrightarrow\sf Volume \ of \ chocolate \ box = 5x \times 4x \times 3x$

$\hookrightarrow\sf 5x \times 4x \ \times 3x = 7500\\\\\hookrightarrow 60x^3 = 7500 \\\\\hookrightarrow x^3 = \dfrac{7500}{60}\\\\\hookrightarrow x^3= \dfrac{750}{6} \\\\\hookrightarrow x^3 = \dfrac{250\times 3}{2\times 3} \\\\\hookrightarrow x^3= \dfrac{250}{2}\\\\\hookrightarrow x^3= 125 \\\\\hookrightarrow x = \sqrt[3]{125} \\\\\hookrightarrow\bf x = 5$

• Length of chocolate box = 5 × 5 = 25 cm

• Breadth of the chocolate box = 4 × 5 = 20 cm

• Height of the chocolate box = 3 × 5 = 15 cm