This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 45 cm has 2 compartments, Q and R, with a water height of 38 cm in Q and 11 cm in R. A hole in the slider caused water to leak from Q to R. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 32 x 38 x 55
= 66880 cm
3 Length of Compartment R
= 80 - 32
= 48 cm
Volume of the water in Compartment R
= 48 x 55 x 11
= 29040 cm
3 Total volume of water
= 66880 + 29040
= 95920 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 95920 ÷ 4400
= 21.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Q
= 38 - 21.8
= 16.2 cm
Drop in the volume of Compartment Q
= 55 x 32 x 16.2
= 28512 cm
3 Volume of water flowed from Q to R in 1 minute
= 28512 ÷ 90
≈ 316.8 cm
3 Answer(s): (a) 21.8 cm; (b) 316.8 cm
3