The figure, not drawn to scale, is made of two connected cubical tanks, X and Y. Tank X is sealed at the top and completely filled to the brim. Tank Y is
34 filled with 100851 mℓ of water. The height of the water level in Tank Y is 1 cm higher than that in Tank X. Height of Tank Y is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 36 cm.
- What is the capacity of Tank Y in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank Y = 100851 mℓ
14 of Tank Y = 100851 ÷ 3 = 33617 mℓ
44 of Tank Y = 33617 x 4 = 134468 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Y = 134468 mℓ = 134.468 ℓ
(b)
Fraction of Tank Y not filled
= 1 -
34 =
14 Height of Tank Y not filled
=
14 x 66 cm
= 16.5 cm
Height of Tank X
= 66 - 16.5 - 1
= 48.5 cm
Volume of remaining water in Tank X
= 48.5 x 48.5 x 36
= 84681 cm
3 Volume of remaining water in Tank Y
= 66 x 66 x 36
= 156816 cm
3 Total volume of remaining water in the tank
= 84681 + 156816
= 241497 cm
3
1 ℓ = 1000 cm
3 241497 cm
3 = 241.497 ℓ
Answer(s): (a) 134.468 ℓ; (b) 241.497 ℓ