This figure is not drawn to scale. A rectangular glass container 90 cm by 52 cm by 50 cm has 2 compartments, K and L, with a water height of 32 cm in K and 13 cm in L. A hole in the slider caused water to leak from K to L. 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 K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 18 x 32 x 52
= 29952 cm
3 Length of Compartment L
= 90 - 18
= 72 cm
Volume of the water in Compartment L
= 72 x 52 x 13
= 48672 cm
3 Total volume of water
= 29952 + 48672
= 78624 cm
3 Base area of the glass container
= 90 x 52
= 4680 cm
2 Height of water
= 78624 ÷ 4680
= 16.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment K
= 32 - 16.8
= 15.2 cm
Drop in the volume of Compartment K
= 52 x 18 x 15.2
= 14227.2 cm
3 Volume of water flowed from K to L in 1 minute
= 14227.2 ÷ 90
≈ 158.1 cm
3 Answer(s): (a) 16.8 cm; (b) 158.1 cm
3