This figure is not drawn to scale. A rectangular glass container 72 cm by 59 cm by 50 cm has 2 compartments, M and N, with a water height of 34 cm in M and 13 cm in N. A hole in the slider caused water to leak from M to N. 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 M to N in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment M
= 36 x 34 x 59
= 72216 cm
3 Length of Compartment N
= 72 - 36
= 36 cm
Volume of the water in Compartment N
= 36 x 59 x 13
= 27612 cm
3 Total volume of water
= 72216 + 27612
= 99828 cm
3 Base area of the glass container
= 72 x 59
= 4248 cm
2 Height of water
= 99828 ÷ 4248
= 23.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 34 - 23.5
= 10.5 cm
Drop in the volume of Compartment M
= 59 x 36 x 10.5
= 22302 cm
3 Volume of water flowed from M to N in 1 minute
= 22302 ÷ 90
≈ 247.8 cm
3 Answer(s): (a) 23.5 cm; (b) 247.8 cm
3