Question

10. In a rectangular solidl:b:h=5:4:2. If its volume
is 1080 cm3, find the dimensions of the solid.​

Answer 1

Solution :

This is a rectangular cuboid .

The length , breadth and height of the cuboid are in the ratio of 5 : 4 : 2 .

Let them be 5x ; 4x and 2x respectively .

The volume of the cuboid Is 1080 cm³ .

> [ Length × Breadth × Height ] = 1080

> [ 5x × 4x × 2x ] = 1080

> 40 x³ = 1080

> 4x³ = 108

> x³ = 27

> x = 3

Length Of Solid ; 5x = 15 cm

Breadth of Solid : 4x = 12 cm .

Height Of Solid : 2x = 6 cm .

This is the required answer .

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$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf 15 \: cm}\put(7.7,6.3){\sf 12\:cm}\put(11.3,7.45){\sf 6\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

Answer 2

Answer:

⠀⠀⠀⌬ l : b : h = 5 : 4 : 2

⠀⠀⠀⌬ Volume = 1080 cm³

⠀⠀⠀⌬ Find the dimensions of solid

Let the length, breadth and height be 5n , 4n and 2n respectively of the solid rectangular cuboid.

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\linethickness{0.4mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{5n}}\put(4,6.3){\sf{4n}}\put(11.2,7.5){\sf{2n}}\put(6.05,7.6){\small\sf{Volume = 1080 cm ^{\sf3} }}\end{picture}$

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Volume=Length \times Breadth \times Height\\\\\\:\implies\sf 1080\:cm^3=5n \times 4n \times 2n\\\\\\:\implies\sf 1080\:cm^3 =40n^3\\\\\\:\implies\sf \dfrac{1080 \:cm^3}{40} =n^3\\\\\\:\implies\sf 27 \:cm^3 = n^3\\\\\\:\implies\sf \sqrt[3]{27 \:cm^3} = n\\\\\\:\implies\sf n = 3 \:cm$

$\rule{200}{1}$

$\underline{\bigstar\:\textsf{Dimensions of the solid rectangular cuboid :}}$

$\bullet\:\:\textsf{Length = 5n = 5(3 cm) = \textbf{15 cm}}\\\bullet\:\:\textsf{Breadth = 4n = 4(3 cm) = \textbf{12 cm}}\\\bullet\:\:\textsf{Height = 2n = 2(3 cm) = \textbf{6 cm}}$