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
45 filled with 139740 mℓ of water. The height of the water level in Tank M is 3 cm higher than that in Tank L. Height of Tank M is 62 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Tank M in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank M = 139740 mℓ
15 of Tank M = 139740 ÷ 4 = 34935 mℓ
55 of Tank M = 34935 x 5 = 174675 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank M = 174675 mℓ = 174.675 ℓ
(b)
Fraction of Tank M not filled
= 1 -
45 =
15 Height of Tank M not filled
=
15 x 62 cm
= 12.4 cm
Height of Tank L
= 62 - 12.4 - 3
= 46.6 cm
Volume of remaining water in Tank L
= 46.6 x 46.6 x 25
= 54289 cm
3 Volume of remaining water in Tank M
= 62 x 62 x 25
= 96100 cm
3 Total volume of remaining water in the tank
= 54289 + 96100
= 150389 cm
3
1 ℓ = 1000 cm
3 150389 cm
3 = 150.389 ℓ
Answer(s): (a) 174.675 ℓ; (b) 150.389 ℓ