The figure, not drawn to scale, is made of two connected cubical tanks, M and N. Tank M is sealed at the top and completely filled to the brim. Tank N is
35 filled with 118923 mℓ of water. The height of the water level in Tank N is 3 cm higher than that in Tank M. Height of Tank N is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 39 cm.
- What is the capacity of Tank N in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank N = 118923 mℓ
15 of Tank N = 118923 ÷ 3 = 39641 mℓ
55 of Tank N = 39641 x 5 = 198205 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 198205 mℓ = 198.205 ℓ
(b)
Fraction of Tank N not filled
= 1 -
35 =
25 Height of Tank N not filled
=
25 x 60 cm
= 24 cm
Height of Tank M
= 60 - 24 - 3
= 33 cm
Volume of remaining water in Tank M
= 33 x 33 x 39
= 42471 cm
3 Volume of remaining water in Tank N
= 60 x 60 x 39
= 140400 cm
3 Total volume of remaining water in the tank
= 42471 + 140400
= 182871 cm
3
1 ℓ = 1000 cm
3 182871 cm
3 = 182.871 ℓ
Answer(s): (a) 198.205 ℓ; (b) 182.871 ℓ