The figure, not drawn to scale, is made of two connected cubical tanks, Y and Z. Tank Y is sealed at the top and completely filled to the brim. Tank Z is
23 filled with 178240 mℓ of water. The height of the water level in Tank Z is 3 cm higher than that in Tank Y. Height of Tank Z is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.
- What is the capacity of Tank Z in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank Z = 178240 mℓ
13 of Tank Z = 178240 ÷ 2 = 89120 mℓ
33 of Tank Z = 89120 x 3 = 267360 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Z = 267360 mℓ = 267.36 ℓ
(b)
Fraction of Tank Z not filled
= 1 -
23 =
13 Height of Tank Z not filled
=
13 x 66 cm
= 22 cm
Height of Tank Y
= 66 - 22 - 3
= 41 cm
Volume of remaining water in Tank Y
= 41 x 41 x 29
= 48749 cm
3 Volume of remaining water in Tank Z
= 66 x 66 x 29
= 126324 cm
3 Total volume of remaining water in the tank
= 48749 + 126324
= 175073 cm
3
1 ℓ = 1000 cm
3 175073 cm
3 = 175.073 ℓ
Answer(s): (a) 267.36 ℓ; (b) 175.073 ℓ