Sir,

Q-1 The rain which falls on roof of 24m * 16m is stored in a cylindrical tank of diametre 14m. If it rains 10 cm on a day, what is the rise of water level in the tank?

Q-2 A water tank built by the municipality of a town to supply water to its 25000 inhabitants at 125 litres per day per person is 40 m long and 31.25 m broad. The tank when full can supply water for 2 days to the inhabitants of the town. Find the depth of the tank.

Q-3 A cuboidal piece of brass having a base of 11 dm2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diametre. Find the length of wire.

Thank you.

1)roof area = 24*16 = 384 m²

It rains 10 cm a day , so the height =  = 0.1 m

Hence, volume of rain = 384*0.1 = 38.4 m³

Radius of cylindrical tank = 14/2 = 7m

Volume of cylindrical tank = r²h

  =  (7)²h

  = *7*7 h

So, volume of rain = volume of cylindrical tank

  38.4 = 22* 7 h

h = 

  = 0.25 m

  = 25 cm

Hence rise of water level = 25 cm

2) Q-2 A water tank built by the municipality of a town to supply water to its 25000 inhabitants at 125 litres per day per person is 40 m long and 31.25 m broad. The tank when full can supply water for 2 days to the inhabitants of the town. Find the depth of the tank.

Total capacity of tank = 25000*125*2 = 6250000 litres

  =  = 6250 m³

Volume of tank = 40 * 31.25 * h m³

 So,  40 * 31.25 * h = 6250

 1250 * h  =  6250

 h =  

  = 5 m

So, the depth of tank = 5m

3) Q-3 A cuboidal piece of brass having a base of 11 dm2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diametre. Find the length of wire.

Area of base of cuboidal brass = 11 dm²

  = 1100cm²

 Height = 0.2 cm = 2cm

Volume of cuboid = 1100* 2 = 2200 cm³

 Diameter of cylinder = 0.25cm

Radius of cylinder =  = 0.125 cm

 Let l be the length of cylindrical wire

So, volume of cylindrical wire = r²h

  =  (0.125)²h

  = *0.125*0.125 h

Volume of cuboid = volume of cylindrical wire

 2200 = *0.125*0.125 h

H = 

  = 44800 cm

  = 448 m