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
34 filled with 129948 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 56 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Tank U in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank U = 129948 mℓ
14 of Tank U = 129948 ÷ 3 = 43316 mℓ
44 of Tank U = 43316 x 4 = 173264 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank U = 173264 mℓ = 173.264 ℓ
(b)
Fraction of Tank U not filled
= 1 -
34 =
14 Height of Tank U not filled
=
14 x 56 cm
= 14 cm
Height of Tank T
= 56 - 14 - 2
= 40 cm
Volume of remaining water in Tank T
= 40 x 40 x 40
= 64000 cm
3 Volume of remaining water in Tank U
= 56 x 56 x 40
= 125440 cm
3 Total volume of remaining water in the tank
= 64000 + 125440
= 189440 cm
3
1 ℓ = 1000 cm
3 189440 cm
3 = 189.44 ℓ
Answer(s): (a) 173.264 ℓ; (b) 189.44 ℓ