Question

3) The total surface of a box is 196 m². If the length and breadth are 8 m and 4 m
respectively. Find the height fo the box?

please help me with this​

Answer 1

A n s w e r

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G i v e n

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• The total surface of a box is 196 sq. m

• Length of the box is 8 m

• Breadth of the box is 4 m

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F i n d

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• The height of the box

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S o l u t i o n

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• Let the height of box be 'h'

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As per the given details we can conclude the box to be a cuboidal box

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Thus ,

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We know that ,

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$\underline{ \underline{\bold{\texttt{Total surface area of cuboid :}}}}$

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➠ A = 2(lb + bh + lh) ⚊⚊⚊⚊ ⓵

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Where ,

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• A = Total surface area of cuboid

• l = Length of cuboid

• b = Breadth of cuboid

• h = Height of cuboid

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$\underline{ \underline{\bold{\texttt{For the given box :}}}}$

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• A = 196 sq. m

• l = 8 m

• b = 4 m

• h = h

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⟮ Putting the above values in ⓵ ⟯

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: ➜ A = 2(lb + bh + lh)

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: ➜ 196 = 2(8(4) + 4(h) + 8(h))

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: ➜ $\sf \dfrac { 196 } { 2 } = (32 + 4h + 8h)$

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: ➜ $\sf 98 = 32 + 12h$

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: ➜ $\sf 12h = 98 - 32$

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: ➜ $\sf 12h = 66$

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: ➜ $\sf h = \dfrac { 66 } { 12 }$

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: : ➨ h = 5.5 m

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• Hence the height of box is 5.5 m

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Additional information

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Volume of cuboid

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• l × b × h

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Where ,

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➻ l = Length of cuboid

➻ b = Breadth of cuboid

➻ h = Height of cuboid

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Curved surface are of cuboid

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• 2h(l + b)

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Where ,

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➻ l = Length of cuboid

➻ b = Breadth of cuboid

➻ h = Height of cuboid

Answer 2

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G i v e n

$\:\:$

• The total surface of a box is 196 sq. m

• Length of the box is 8 m

• Breadth of the box is 4 m

$\:\:$

F i n d

$\:\:$

• The height of the box

$\:\:$

S o l u t i o n

$\:\:$

Let the height of box be 'h'

$\:\:$

As per the given details we can conclude the box to be a cuboidal box

$\:\:$

Thus ,

$\:\:$

We know that ,

$\:\:$

$\underline{ \underline{\bold{\texttt{Total surface area of cuboid :}}}}$

$\:\:$

➠ A = 2(lb + bh + lh) ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

A = Total surface area of cuboid

l = Length of cuboid

b = Breadth of cuboid

h = Height of cuboid

$\:\:$

$\underline{ \underline{\bold{\texttt{For the given box :}}}}$

$\:\:$

A = 196 sq. m

l = 8 m

b = 4 m

h = h

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ A = 2(lb + bh + lh)

$\:\:$

: ➜ 196 = 2(8(4) + 4(h) + 8(h))

$\:\:$

: ➜ $\sf \dfrac { 196 } { 2 } = (32 + 4h + 8h)$

$\:\:$

: ➜ $\sf 98 = 32 + 12h$

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: ➜ $\sf 12h = 98 - 32$

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: ➜ $\sf 12h = 66$

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: ➜ $\sf h = \dfrac { 66 } { 12 }$

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: : ➨ h = 5.5 m

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• Hence the height of box is 5.5 m

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