This figure is not drawn to scale. A rectangular glass tank 76 cm by 56 cm by 47 cm has 2 compartments, B and C, with a water height of 39 cm in B and 11 cm in C. A hole in the slider caused water to leak from B to C. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank now?
- It took 134 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from B to C in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment B
= 19 x 39 x 56
= 41496 cm
3 Length of Compartment C
= 76 - 19
= 57 cm
Volume of the water in Compartment C
= 57 x 56 x 11
= 35112 cm
3 Total volume of water
= 41496 + 35112
= 76608 cm
3 Base area of the glass tank
= 76 x 56
= 4256 cm
2 Height of water
= 76608 ÷ 4256
= 18 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment B
= 39 - 18
= 21 cm
Drop in the volume of Compartment B
= 56 x 19 x 21
= 22344 cm
3 Volume of water flowed from B to C in 1 minute
= 22344 ÷ 105
≈ 212.8 cm
3 Answer(s): (a) 18 cm; (b) 212.8 cm
3