This figure is not drawn to scale. A rectangular glass tank 88 cm by 54 cm by 44 cm has 2 compartments, Q and R, with a water height of 33 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 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 36 x 33 x 54
= 64152 cm
3 Length of Compartment R
= 88 - 36
= 52 cm
Volume of the water in Compartment R
= 52 x 54 x 11
= 30888 cm
3 Total volume of water
= 64152 + 30888
= 95040 cm
3 Base area of the glass tank
= 88 x 54
= 4752 cm
2 Height of water
= 95040 ÷ 4752
= 20 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment Q
= 33 - 20
= 13 cm
Drop in the volume of Compartment Q
= 54 x 36 x 13
= 25272 cm
3 Volume of water flowed from Q to R in 1 minute
= 25272 ÷ 105
≈ 240.7 cm
3 Answer(s): (a) 20 cm; (b) 240.7 cm
3