Question

There is a hemispherical roof on the cylindrical room. The maximum height of the room is 20 m. If the inner diameter of the floor is equal to the maximum height of the room, then find the volume of air in the room. (Use л = 3.14)

Answer 1

Given:

Maximum height of the room = 20 m

Inner diameter of floor = 20 m

∴ `r = 20/2 = 10`

π = 3.14

Since the roof is hemispherical, its height = r =10 m

∴ Height of cylindrical part

h = 20 − 10 = 10 m

Volume of air in the room

V = Volume of cylinder + Volume of hemisphere

1) Volume of cylinder

V1​ = πr²h = 3.14 × 10² × 10 = 3.14 × 100 × 10 = 3140 m³

2) Volume of a hemisphere

`V_2​ = 2/3 πr^3 = 2/3 xx 3.14 xx 10^3 = 2/3 xx 3.14 xx 1000 = 6280/3 = 2093.33 m^3`

Total volume:

V = 3140 + 2093.33

= 5233.33 m³