Question

the length and breadth and height of a chocolate box are in the ratio 5:4:3 if its volume is 7500 cubic cm then find its dimensions

Answer 1

Given: Ratio of Length, breadth and height of a chocolate box are 5:4:3. And, Volume of chocolate box is 7500 cm³.

Need to find: Dimensions of chocolate box?

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❍ Let's consider Length, Breadth and height of chocolate box be 5x, 4x and 3x cm.

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As we know that,

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$\star\:{\underline{\boxed{\frak{Volume_{\:(Cuboid)} = Length \times breadth \times Height}}}}\\\\ \\:\implies\sf 7500 = 5x \times 4x \times 3x\\\\\\ :\implies\sf 7500 = 60x^3 \\\\\\ :\implies\sf x^3 = \cancel{\dfrac{7500}{60}}\\\\\\:\implies\sf x^3 = 125\\\\\\ :\implies\sf x = \sqrt[3]{125}\\\\\\ :\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\:\bigstar$

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Therefore,

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• Length of chocolate box, 5x = 5 × 5 = 25 cm
• Breadth of chocolate box, 4x = 4 × 5 = 20 cm
• Height of chocolate box, 3x = 3 × 5 = 15 cm

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$\therefore$ Hence, Dimensions of chocolate box are 25 cm, 20 cm & 15 cm respectively.

Answer 2

${\bf{Given\::}}$

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

• Volume of the chocolate box is 7500 cm³.

$\\ {\bf{To\: Find\::}}$

• The dimension of the chocolate box.

$\\ {\bf{Solution\::}}$

Let,

⠀⠀⠀⑴ Length of the box is 5x.

⠀⠀⠀⑵ Breadth of the box is 4x.

⠀⠀⠀⑶ Height of the box is 3x.

As we know that,

➣ Volume of the chocolate box is given as,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Volume\:=\:Length\times{Breadth}\times{Height} \:}\:{\Large\mid}\:\green\bigstar$

➠ 7500 = 5x × 4x × 3x

➠ 7500 = 60 x³

➠ x³ = $\tt{\dfrac{7500}{60}}$

➠ x = $\tt{\sqrt[3]{125}}$

➠ x = $\bf{5}$

Hence,

➳ ⑴ Length = 5x = 5 × 5 = 25 cm

➳ ⑵ Breadth = 4x = 4 × 5 = 20 cm

➳ ⑶ Height = 3x = 3 × 5 = 15 cm

Therefore,

⠀⠀⠀⑴ Length of the box is 25 cm.

⠀⠀⠀⑵ Breadth of the box is 20 cm.

⠀⠀⠀⑶ Height of the box is 15 cm.