This figure is not drawn to scale. A rectangular glass container 84 cm by 57 cm by 44 cm has 2 compartments, K and L, with a water height of 37 cm in K and 16 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 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 K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 18 x 37 x 57
= 37962 cm
3 Length of Compartment L
= 84 - 18
= 66 cm
Volume of the water in Compartment L
= 66 x 57 x 16
= 60192 cm
3 Total volume of water
= 37962 + 60192
= 98154 cm
3 Base area of the glass container
= 84 x 57
= 4788 cm
2 Height of water
= 98154 ÷ 4788
= 20.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment K
= 37 - 20.5
= 16.5 cm
Drop in the volume of Compartment K
= 57 x 18 x 16.5
= 16929 cm
3 Volume of water flowed from K to L in 1 minute
= 16929 ÷ 105
≈ 161.2 cm
3 Answer(s): (a) 20.5 cm; (b) 161.2 cm
3