Question

The area of the 4walls of a room is 77 square. the length and breath of the room are 7.5m and 3.5m respectively. Find the height of the room.​

Answer 1

Given :-

• The area of the 4walls of a room is 77 square. the length and breath of the room are 7.5m and 3.5m respectively.

To find :-

• Height of the room

Solution :-

• Area of the four walls of a room = 77m²

• Length of room = 7.5 m

• Breadth of room = 3.5 m

As we know that

→ Lateral surface area of cuboid = Area of four walls of room

→ Lateral surface of cuboid = 2(l + b)h

Where " l " is length, " b " is breadth, " h " is height of cuboid.

According to question

→ Lateral surface of room = 77

→ 2(l + b)h = 77

Put the value of length and breadth

→ 2(7.5 + 3.5)h = 77

→ 2 × 11 × h = 77

→ 22h = 77

→ h = 77/22

→ h = 7/2

→ h = 3.5 m

Hence,

• Height of room is 3.5 m

Verification :-

• Length = 7.5m
• Breadth = 3.5m
• Height = 3.5m

→ Lateral surface area of room

→ 2(l + b)h

Substitute the values

→ 2(7.5 + 3.5) × 3.5

→ 2 × 11 × 3.5

→ 22 × 3.5

→ 77m²

• Hence, verified

Answer 2

Given area of the 4 walls of a room is 77 m².

Length and breadth of room are 7.5m and 3.5m respectively.

We have to find, height of the room.

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☯ Room is in cuboidal shape.

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

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★ Area of four walls = C.S.A. of room

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Therefore,

$\star\;{\boxed{\sf{\purple{CSA_{\;(cuboid)} = 2(l + b)h}}}}$

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Here,

• CSA = 77 m²
• Length = 7.5 m
• Breadth = 3.5 m

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⋆ Reference of image is shown in diagram

$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{7.5 m}}\put(4,6.3){\sf{3.5 m}}\put(10.7,7.5){\sf{h}}\end{picture}$

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$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf 2(7.5 + 3.5)h = 77$

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$:\implies\sf 2h(11) = 77$

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$:\implies\sf 22h = 77$

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$:\implies\sf h = \cancel{ \dfrac{77}{22}}$

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$:\implies{\underline{\boxed{\sf{\purple{h = 3.5\;m}}}}}\;\bigstar$

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$\therefore$ Hence, Height of room is 3.5 m.

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Additional Information:

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• T.S.A. of cuboid = 2(lb + bh + hl)
• Volume of cuboid = lbh
• T.S.A of cube = 6a²
• C.S.A. of cube = 4a²
• Volume of cube = a³
• T.S.A. of cylinder = 2πr(r + h)
• C.S.A. of cylinder = 2πrh
• Volume of cylinder = πr²h