This figure is not drawn to scale. A rectangular glass container 90 cm by 58 cm by 48 cm has 2 compartments, M and N, with a water height of 36 cm in M and 18 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
= 34 x 36 x 58
= 70992 cm
3 Length of Compartment N
= 90 - 34
= 56 cm
Volume of the water in Compartment N
= 56 x 58 x 18
= 58464 cm
3 Total volume of water
= 70992 + 58464
= 129456 cm
3 Base area of the glass container
= 90 x 58
= 5220 cm
2 Height of water
= 129456 ÷ 5220
= 24.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 36 - 24.8
= 11.2 cm
Drop in the volume of Compartment M
= 58 x 34 x 11.2
= 22086.4 cm
3 Volume of water flowed from M to N in 1 minute
= 22086.4 ÷ 90
≈ 245.4 cm
3 Answer(s): (a) 24.8 cm; (b) 245.4 cm
3