Question

If the ratio of length , breadth and height of a cuboid is 2:3:4 and its volume is 192 m³ .Find its dimensions​

Answer 1

Answer:

let length of cuboid = 2x

breadth of cuboid = 3x

height of cuboid = 4x

so,

volume of cuboid = L×B×H

192 m^3 = 2x × 3x × 4x

192 m^3= 24x m^3

192/24 = x

8 m = x

length of cuboid= 2(8)= 16m

breadth of cuboid=3(8)= 24m

height of cuboid = 4(8)= 32m

Answer 2

Given:

1. Ratio of Length, Breadth and Height = 2:3:4
2. Volume = 192 m³

To find:

• Dimensions

Method:

$\tt{Let \: the \: Length,\: Breadth \: and \: Height \: be \: 2x, \: 3x \: and \: 4x}\\\\\\\rm{According \: to \: the \: question;}\\\\\\\bf{Volume \: of \: cuboid = Length \times Breadth \times Height}\\\\\\\dashrightarrow \sf{192 m^{3} = 2x \times 3x \times 4x }\\\\\\\longrightarrow \sf{192 = 24 \: x^{3} }\\\\\\:\implies \sf{x^{3} = \dfrac{192}{24} }\\\\\\:\implies \sf{x^{3} = 8}\\\\\\:\implies \sf{x = \sqrt[3]{8} }\\\\\\:\implies \sf{x = \pm 2}$

$Side \: cannot \: be \: negative\\\\\therefore \boxed{\bf{x = 2 \: m}}\\\\\\\\\underline{\rm{For \: finding \: the \: dimensions;}}\\\\\bullet \sf{Length = 2x = 2 \times 2 = \bold{\underline{4m}}}\\\\\bullet \sf{Breadth = 3x = 3 \times 2 = \bold{\underline{6m}}}\\\\\bullet \sf{Height = 4x = 4 \times 2 = \bold{\underline{8m}}}$

∴ The dimensions are 4m, 6m, 8m