Question

The length of a hall is 15 m and width is 12 m. The sum of the areas of the floor and flat root is equal to the sum of the areas of the four walls. The capacity of the hall is ________.

Answer 1

Let the height of hall be h m.

Length of the hall, l = 15 m

Width of the hall, b = 12 m

Now,

Area of the floor + Area of the flat roof = Sum of the areas of the four walls

⇒ lb + lb = 2h(l + b)

⇒ 2lb = 2h(l + b)

⇒ 15 m × 12 m = h(15 m + 12 m)

⇒ h = $\frac{15\times 12}{27}$ = $\frac{20}{3}$ m

∴ Capacity of the hall = lbh = $15\mathrm{m}\times 12\mathrm{m}\times \frac{20}{3}\mathrm{m}$ = 1200 m³

Thus, the capacity of the hall is 1200 m³.

The length of a hall is 15 m and width is 12 m. The sum of the areas of the floor and flat root is equal to the sum of the areas of the four walls. The capacity of the hall is ___1200 m³___.