This figure is not drawn to scale. A rectangular glass container 72 cm by 50 cm by 50 cm has 2 compartments, C and D, with a water height of 32 cm in C and 14 cm in D. A hole in the slider caused water to leak from C to D. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the container now?
- It took 112 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 C to D in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment C
= 24 x 32 x 50
= 38400 cm
3 Length of Compartment D
= 72 - 24
= 48 cm
Volume of the water in Compartment D
= 48 x 50 x 14
= 33600 cm
3 Total volume of water
= 38400 + 33600
= 72000 cm
3 Base area of the glass container
= 72 x 50
= 3600 cm
2 Height of water
= 72000 ÷ 3600
= 20 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment C
= 32 - 20
= 12 cm
Drop in the volume of Compartment C
= 50 x 24 x 12
= 14400 cm
3 Volume of water flowed from C to D in 1 minute
= 14400 ÷ 90
≈ 160.0 cm
3 Answer(s): (a) 20 cm; (b) 160.0 cm
3