Question

The length of a cinema hall is 20 m and width is 16 m. The sum of the area of its floor and roof is equal to the surface area of its four wall. Find the volume and height of the hall.

Answer 1

Let the height of the walls of the room be hLength of the room, l = 20 mWidth of the room, b = 16 m

Sum of the areas of the floor and the flat roof = lb + lb = 2lb = 2 × 20 m × 16 m = 640 m2Sum of areas of 4 walls = 2h × (l + b) = 2h × (20 m + 16 m) = 72h mAccording to the given information 72h m = 640 m2

⇒h=640/72m=80/9m=8.9m (approx)
Thus, height of the wall is approximately 8.9 m

Answer 2

area of base =lb= 16×20=320
area of top = also 320
l. surface area = 640
l.s.a=2 (l+b)h=640
2 (36)h=640
h=640/72
=8.88m
volume =lbh= 2841.6 m^3