Question

The base of a house has area 110 m². One night 12 mm of rain falls on the roof. All of the water goes into a tank which has base diameter 4 m.
a Find the volume of water which fell on the roof.
b. How many KL of water entered the tank?
c. By how much did the water level in the tank rise?​

Answer 1

Answer:

a. 1.32 m³

b. 1.32 kL

c. 105.04 m

Step-by-step explanation:

Area of roof = 110 m²

Rain fall = 12mm = (12/1000)m = 0.012 m

(a) Volume of water that fell on roof = Area of roof × Rain depth

    = 110 × 0.012

    = 1.32 m³

(b) 1 m³ = 1 kL

 ∴ 1.32 m³ = 1.32 kL

(c) Radius of tank = (4/2) = 2 m

    Volume of tank = Base area × Height

     = πr²h

     = π × (2)² × h

     = 4πh

     The volume added to the tank must be equal to the volume which falls on roof.

     i.e. Volume of tank = Volume of water that fell on roof

      or, 4πh = 1.32

      or, h = 1.32 / (4π)

      ∴   h = 0.10504 m = (0.10504/100)cm = 10.504 cm

∴ The water level rises by about 10.504 cm.