Question

the length of hall is 24m and width is 16m the sum of areas of the floor flat and the roof it equal to the are of four wall.find the height and the volume of the hall

Answer 1

Length = 24 m
Width = 16 m
Height = h

Given that,
The sum of area of roof and floor = Sum of area of four walls

2lb = 2(bh + hl)
lb = bh + hl
16 × 24 = 16h + 24h
384 = 40h
h = 9.6 m


Volume = l × b × h = 24 × 16 × 9.6 = 3686.4 m³

Answer 2

$\sf\underline{Answer:}$

$\sf{Let\:the\:height\:of\:the\:hall\:be\:h\:m\:.Then,}$

$\sf{Sum\:of\:area\:of\:4\:walls=\:2(l+b)h\:m^2}$

$\leadsto$ $\sf{2(20+16)h\:m^2}$

$\leadsto$ $\sf\underline{72h\:m^2}$

_____________

Sum of the areas of the floor and the flat roof

$\leadsto$ $\sf{(20\times16+20\times16)m^2}$

$\sf{640\:m^2}$

It is given that the sum of the areas of four walls is equal to the sum of the areas of the floor and roof.

$\therefore$ $\sf\qquad{72h=640}$

$\sf\qquad{h=}$ $\sf\cancel\dfrac{640}{72}m$

$\sf\qquad{=8.88m}$

________________

$\text{So,\:\:height\:\:of\:\:the\:\:hall=8.88m}$

$\sf\qquad{Volume\:of\:the\:hall,}$

$\sf\qquad{20\times16\times80/9\:m^3}$

$\sf\qquad\cancel\dfrac{25600}{9}m^3$ = $\sf\underline{2844.4\:\:m^3}$