This figure is not drawn to scale. A rectangular glass container 72 cm by 58 cm by 48 cm has 2 compartments, K and L, with a water height of 32 cm in K and 14 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 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 K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 14 x 32 x 58
= 25984 cm
3 Length of Compartment L
= 72 - 14
= 58 cm
Volume of the water in Compartment L
= 58 x 58 x 14
= 47096 cm
3 Total volume of water
= 25984 + 47096
= 73080 cm
3 Base area of the glass container
= 72 x 58
= 4176 cm
2 Height of water
= 73080 ÷ 4176
= 17.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment K
= 32 - 17.5
= 14.5 cm
Drop in the volume of Compartment K
= 58 x 14 x 14.5
= 11774 cm
3 Volume of water flowed from K to L in 1 minute
= 11774 ÷ 72
≈ 163.5 cm
3 Answer(s): (a) 17.5 cm; (b) 163.5 cm
3