This figure is not drawn to scale. A rectangular glass container 80 cm by 52 cm by 47 cm has 2 compartments, C and D, with a water height of 32 cm in C and 13 cm in D. A hole in the slider caused water to leak from C to D. 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 C to D in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment C
= 40 x 32 x 52
= 66560 cm
3 Length of Compartment D
= 80 - 40
= 40 cm
Volume of the water in Compartment D
= 40 x 52 x 13
= 27040 cm
3 Total volume of water
= 66560 + 27040
= 93600 cm
3 Base area of the glass container
= 80 x 52
= 4160 cm
2 Height of water
= 93600 ÷ 4160
= 22.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment C
= 32 - 22.5
= 9.5 cm
Drop in the volume of Compartment C
= 52 x 40 x 9.5
= 19760 cm
3 Volume of water flowed from C to D in 1 minute
= 19760 ÷ 90
≈ 219.6 cm
3 Answer(s): (a) 22.5 cm; (b) 219.6 cm
3