The dimensions of a cuboid are in the ration 4 : 5 : 6 and its surface area is

5328 m2



Find (i)

2 thoughts on “The dimensions of a cuboid are in the ration 4 : 5 : 6 and its surface area is <br /><br />5328 m2<br /><br /><br /><br />Find (i)”

1. Answer:

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2. [tex] \huge{ \mid{ \boxed{ \sf{Question:- }}}} \mid[/tex]

   • The dimensions of a cuboid are in the ration 4 : 5 : 6 and its surface area is 5328 m²

   • Find (i) its length, breadth and height, (ii) its volume and (iii) the length of a diagonal.

   [tex] \huge \bf{ \underline{Given}}[/tex]

   • Surface Area of cuboid is 5328m²
   • Dimensions are in the ratio of 4:5:6

   To find:–

   • It’s length, breadth and height
   • The length of diagonal

   Solution:-

   Let the dimensions be 4x, 5x, 6x

   We know that

   • Surface area of cuboid =2(lb+bh+hl)

   [tex] \: \: \: \: \: \: \: \bf \: \implies \: 2(4x \times 5x + 5x \times 6x + 6x \times 4x) = 5328 {m}^{2} [/tex]

   [tex] \: \: \: \: \: \: \: \: \sf{ \red{\implies \: 2(20 {x}^{2} + 30 {x}^{2} + 24 {x}^{2} ) = 5328}}[/tex]

   [tex] \: \: \: \: \: \: \sf \implies \: 148 {x}^{2} = 5328[/tex]

   [tex] \: \: \: \: \: \: \implies \sf \: x² = 36[/tex]

   [tex] \: \: \: \: \: \implies \sf \: x = \sqrt{36} = 6[/tex]

   Therefore the required value for x is 6

   Now the dimensions are:-

   • Length of cuboid = 6×4=24m
   • Breadth of cuboid =6×5=30m
   • Height of cuboid =6×6=36m

   Diagonal of cuboid:–

   Formula used⬇️

   [tex] \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow\sqrt{( {l}^{2} + {b}^{2} + {h}^{2}) } [/tex]

   [tex] \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ ({24}^{2} + {30}^{2} + {36}^{2}) } [/tex]

   [tex] \: \: \: \: \: \: \: \: \: \: \: = \sqrt{576 + 900 + 1296} [/tex]

   [tex] \: \: \: \: \: \: \: \: \: \: \: \approx52.172[/tex]

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   More formulas:-

   Surface area formulas ✔✔:-

   • Surface area of cuboid =2(lb+bh+hl)
   • Surface area of cube=6a²
   • Right Circular Cone= 2πr(h+r)
   • Sphere =4πr²
   • Right circular cone= πr(l+r)
   • Hemisphere = 3πr²

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