This figure is not drawn to scale. A rectangular glass container 84 cm by 55 cm by 48 cm has 2 compartments, L and M, with a water height of 33 cm in L and 12 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 134 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
= 26 x 33 x 55
= 47190 cm
3 Length of Compartment M
= 84 - 26
= 58 cm
Volume of the water in Compartment M
= 58 x 55 x 12
= 38280 cm
3 Total volume of water
= 47190 + 38280
= 85470 cm
3 Base area of the glass container
= 84 x 55
= 4620 cm
2 Height of water
= 85470 ÷ 4620
= 18.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment L
= 33 - 18.5
= 14.5 cm
Drop in the volume of Compartment L
= 55 x 26 x 14.5
= 20735 cm
3 Volume of water flowed from L to M in 1 minute
= 20735 ÷ 105
≈ 197.5 cm
3 Answer(s): (a) 18.5 cm; (b) 197.5 cm
3