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 159590 mℓ of water. The height of the water level in Tank U is 3 cm higher than that in Tank T. Height of Tank U is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 35 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 = 159590 mℓ
13 of Tank U = 159590 ÷ 2 = 79795 mℓ
33 of Tank U = 79795 x 3 = 239385 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank U = 239385 mℓ = 239.385 ℓ
(b)
Fraction of Tank U not filled
= 1 -
23 =
13 Height of Tank U not filled
=
13 x 66 cm
= 22 cm
Height of Tank T
= 66 - 22 - 3
= 41 cm
Volume of remaining water in Tank T
= 41 x 41 x 35
= 58835 cm
3 Volume of remaining water in Tank U
= 66 x 66 x 35
= 152460 cm
3 Total volume of remaining water in the tank
= 58835 + 152460
= 211295 cm
3
1 ℓ = 1000 cm
3 211295 cm
3 = 211.295 ℓ
Answer(s): (a) 239.385 ℓ; (b) 211.295 ℓ