Question

the length of a hall is 15 m long and 12 m broad. If the sum of the area of floor and ceiling is equal to the areas of four walls .find the height and volume of hall ?​

Answer 1

GivEn:

• Length of hall = 15 m
• Breadth of hall = 12 m

To find:

• Height and Volume of hall?

Solution:

★ Area of floor and ceiling,

➻ 2 × (l × b)

➻ 2 × (15 × 12)

➻ 2 × 180

➻ 360 m²

★ Now, Finding area of four walls and ceiling,

We know that,

Area of four walls = Curved surface area of hall

Therefore,

Area of four walls = 2(15 + 12)h

➻ 2 × 27 × h

➻ 54h m²

★ According to the Question:

Area of four walls and ceiling is equal to the areas of four walls

Therefore,

➻ 360 = 54h

➻ h = 360/54

➻ h = 6.6666667

➻ h ≈ 6.667 m

Hence, Height of hall is 6.667 m (approx) .

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• Volume of hall,

We know that,

hall is in cuboidal shape.

Volume of cuboid = l × b × h

Here,

• Length, l = 15 m
• Breadth, b = 12 m
• Height, h = 6.667 m

Putting values,

➻ 15 × 12 × 6.667

➻ 1200 m³

Hence, Volume of hall is 1200 m³ (approx).

Answer 2

$\Large{\underline{\underline{\sf{Given:-}}}}$

☞ Length of Hall = 15m

☞ Breadth of Hall = 12m

☞ ᴀʀᴇᴀ ᴏꜰ ꜰʟᴏᴏʀ+ᴀʀᴇᴀ ᴏꜰ ᴄᴇɪʟɪɴɢ = ᴀʀᴇᴀ ᴏꜰ ꜰᴏᴜʀ ᴡᴀʟʟꜱ.

$\Large{\underline{\underline{\sf{To\;Find:-}}}}$

☞ Height & Volume of hall.

$\Large{\underline{\underline{\sf{Required\; Response:-}}}}$

Let's,

Length, Breadth and Height of the hall be l,b & h respectively.

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ꜱᴜᴍ

$→\;{\sf{lb+lb = 2h(l+b)}}$

$→\;{\sf{2(lb) = 2h(l+b)}}$

$→\;{\sf{lb = h(l+b)}}$

$→\;{\sf{h = \frac{lb}{(l+b)}}}$

$→\;{\sf{h = \frac{15×12}{(15+12)}}}$

$→\;{\sf{h = \frac{15×12}{27}}}$

$→\;{\sf{h = \frac{5×4}{3}}}$

$➝\;\Large{\pink{\bf{h = \frac{20}{3}m}}}$

Volume of Hall = lbh.

$→\;{\sf{15×12×\frac{20}{3}}}$

$→\;{\sf{15×4×20}}$

$➝\;\Large{\red{\bf{1200m³}}}$

Hope It Helps You ✌️