This figure is not drawn to scale. A rectangular glass container 72 cm by 51 cm by 45 cm has 2 compartments, L and M, with a water height of 36 cm in L and 18 cm in M. A hole in the slider caused water to leak from L to M. 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 L to M in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment L
= 38 x 36 x 51
= 69768 cm
3 Length of Compartment M
= 72 - 38
= 34 cm
Volume of the water in Compartment M
= 34 x 51 x 18
= 31212 cm
3 Total volume of water
= 69768 + 31212
= 100980 cm
3 Base area of the glass container
= 72 x 51
= 3672 cm
2 Height of water
= 100980 ÷ 3672
= 27.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment L
= 36 - 27.5
= 8.5 cm
Drop in the volume of Compartment L
= 51 x 38 x 8.5
= 16473 cm
3 Volume of water flowed from L to M in 1 minute
= 16473 ÷ 72
≈ 228.8 cm
3 Answer(s): (a) 27.5 cm; (b) 228.8 cm
3