This figure is not drawn to scale. A rectangular glass container 77 cm by 55 cm by 40 cm has 2 compartments, M and N, with a water height of 36 cm in M and 15 cm in N. A hole in the slider caused water to leak from M to N. 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 M to N in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment M
= 22 x 36 x 55
= 43560 cm
3 Length of Compartment N
= 77 - 22
= 55 cm
Volume of the water in Compartment N
= 55 x 55 x 15
= 45375 cm
3 Total volume of water
= 43560 + 45375
= 88935 cm
3 Base area of the glass container
= 77 x 55
= 4235 cm
2 Height of water
= 88935 ÷ 4235
= 21 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment M
= 36 - 21
= 15 cm
Drop in the volume of Compartment M
= 55 x 22 x 15
= 18150 cm
3 Volume of water flowed from M to N in 1 minute
= 18150 ÷ 105
≈ 172.9 cm
3 Answer(s): (a) 21 cm; (b) 172.9 cm
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