Find the height of the gymnasium ceiling if its volume is 5465.6 m2 and the floor area is 854 m2.

Given:

V = 5465.6 m ^ 3,

S = 854 m ^ 2.

Find – h.

Solution.

Let’s assume that the room has the shape of a rectangular parallelepiped.

By definition of the volume of a rectangular parallelepiped:

V = a * b * h. (1)

Where a – width, b – length, h – height.

By definition of area:

S = a * b. (2)

Substitute formula (2) into formula (1):

V = S * h. (3)

From formula (3) we express the height h:

h = V / S. (4)

Substitute numerical values into formula (4) and find the height of the room:

h = 5465.6 / 854 = 6.4 (m).

Answer: h = 6.4 m.