This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 45 cm has 2 compartments, B and C, with a water height of 32 cm in B and 12 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 container now?
- It took 115 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
= 18 x 32 x 55
= 31680 cm
3 Length of Compartment C
= 80 - 18
= 62 cm
Volume of the water in Compartment C
= 62 x 55 x 12
= 40920 cm
3 Total volume of water
= 31680 + 40920
= 72600 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 72600 ÷ 4400
= 16.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment B
= 32 - 16.5
= 15.5 cm
Drop in the volume of Compartment B
= 55 x 18 x 15.5
= 15345 cm
3 Volume of water flowed from B to C in 1 minute
= 15345 ÷ 72
≈ 213.1 cm
3 Answer(s): (a) 16.5 cm; (b) 213.1 cm
3