Question

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.​

Answer 1

$\huge{ \mid{ \boxed{ \sf{Question:- }}}} \mid$

• 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.

$\huge \bf{ \underline{Given}}$

• 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)

$\: \: \: \: \: \: \: \bf \: \implies \: 2(4x \times 5x + 5x \times 6x + 6x \times 4x) = 5328 {m}^{2}$

$\: \: \: \: \: \: \: \: \sf{ \red{\implies \: 2(20 {x}^{2} + 30 {x}^{2} + 24 {x}^{2} ) = 5328}}$

$\: \: \: \: \: \: \sf \implies \: 148 {x}^{2} = 5328$

$\: \: \: \: \: \: \implies \sf \: x² = 36$

$\: \: \: \: \: \implies \sf \: x = \sqrt{36} = 6$

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⬇️

$\: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow\sqrt{( {l}^{2} + {b}^{2} + {h}^{2}) }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ ({24}^{2} + {30}^{2} + {36}^{2}) }$

$\: \: \: \: \: \: \: \: \: \: \: = \sqrt{576 + 900 + 1296}$

$\: \: \: \: \: \: \: \: \: \: \: \approx52.172$

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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

Answer 2

Answer:

what is Gravity?

Step-by-step explanation:

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