This figure is not drawn to scale. A rectangular glass container 80 cm by 52 cm by 49 cm has 2 compartments, B and C, with a water height of 32 cm in B and 20 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
= 16 x 32 x 52
= 26624 cm
3 Length of Compartment C
= 80 - 16
= 64 cm
Volume of the water in Compartment C
= 64 x 52 x 20
= 66560 cm
3 Total volume of water
= 26624 + 66560
= 93184 cm
3 Base area of the glass container
= 80 x 52
= 4160 cm
2 Height of water
= 93184 ÷ 4160
= 22.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment B
= 32 - 22.4
= 9.6 cm
Drop in the volume of Compartment B
= 52 x 16 x 9.6
= 7987.2 cm
3 Volume of water flowed from B to C in 1 minute
= 7987.2 ÷ 72
≈ 110.9 cm
3 Answer(s): (a) 22.4 cm; (b) 110.9 cm
3