The figure, not drawn to scale, is made of two connected cubical tanks, T and U. Tank T is sealed at the top and completely filled to the brim. Tank U is
23 filled with 147118 mℓ of water. The height of the water level in Tank U is 2 cm higher than that in Tank T. Height of Tank U is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 26 cm.
- What is the capacity of Tank U in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank U = 147118 mℓ
13 of Tank U = 147118 ÷ 2 = 73559 mℓ
33 of Tank U = 73559 x 3 = 220677 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank U = 220677 mℓ = 220.677 ℓ
(b)
Fraction of Tank U not filled
= 1 -
23 =
13 Height of Tank U not filled
=
13 x 69 cm
= 23 cm
Height of Tank T
= 69 - 23 - 2
= 44 cm
Volume of remaining water in Tank T
= 44 x 44 x 26
= 50336 cm
3 Volume of remaining water in Tank U
= 69 x 69 x 26
= 123786 cm
3 Total volume of remaining water in the tank
= 50336 + 123786
= 174122 cm
3
1 ℓ = 1000 cm
3 174122 cm
3 = 174.122 ℓ
Answer(s): (a) 220.677 ℓ; (b) 174.122 ℓ