The figure, not drawn to scale, is made of two connected cubical tanks, L and M. Tank L is sealed at the top and completely filled to the brim. Tank M is
35 filled with 123708 mℓ of water. The height of the water level in Tank M is 5 cm higher than that in Tank L. Height of Tank M is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 23 cm.
- What is the capacity of Tank M in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank M = 123708 mℓ
15 of Tank M = 123708 ÷ 3 = 41236 mℓ
55 of Tank M = 41236 x 5 = 206180 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank M = 206180 mℓ = 206.18 ℓ
(b)
Fraction of Tank M not filled
= 1 -
35 =
25 Height of Tank M not filled
=
25 x 60 cm
= 24 cm
Height of Tank L
= 60 - 24 - 5
= 31 cm
Volume of remaining water in Tank L
= 31 x 31 x 23
= 22103 cm
3 Volume of remaining water in Tank M
= 60 x 60 x 23
= 82800 cm
3 Total volume of remaining water in the tank
= 22103 + 82800
= 104903 cm
3
1 ℓ = 1000 cm
3 104903 cm
3 = 104.903 ℓ
Answer(s): (a) 206.18 ℓ; (b) 104.903 ℓ