Question

the length of a hall is 20m and width is 16m. The sum of areas of floor and roof is equal to the sum of areas of four walls. find the height and volume of the hall.

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

${\boxed{\sf\:{Dimensions}}}$

Length = 20m

Breadth = 16m

${\boxed{\sf\:{Assumption}}}$

Height = h

Situation

${\boxed{\sf\:{Area\;of\;floor + Area\;of\;ceiling = Area\; of\;4\;walls}}}$

l × b + l × b = 2(l + b)h

${\boxed{\sf\:{Substitute\;the\;values}}}$

20 × 16 + 20 × 16 = 2(20 + 16)h

320 + 320 = 2 × 36h

640 = 2 × 36h

$\tt{\rightarrow h=\dfrac{640}{2\times 36}}$

$\tt{\rightarrow h=\dfrac{80}{9}}$

= 8.89m

Now,

Volume = l × b × h

$\tt{\rightarrow 20\times 16\times\dfrac{80}{9}}$

$\tt{\rightarrow\dfrac{25600}{9}}$

= 2844.4 m³