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
23 filled with 188008 mℓ of water. The height of the water level in Tank Y is 3 cm higher than that in Tank X. Height of Tank Y is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 23 cm.
- What is the capacity of Tank Y in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank Y = 188008 mℓ
13 of Tank Y = 188008 ÷ 2 = 94004 mℓ
33 of Tank Y = 94004 x 3 = 282012 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Y = 282012 mℓ = 282.012 ℓ
(b)
Fraction of Tank Y not filled
= 1 -
23 =
13 Height of Tank Y not filled
=
13 x 69 cm
= 23 cm
Height of Tank X
= 69 - 23 - 3
= 43 cm
Volume of remaining water in Tank X
= 43 x 43 x 23
= 42527 cm
3 Volume of remaining water in Tank Y
= 69 x 69 x 23
= 109503 cm
3 Total volume of remaining water in the tank
= 42527 + 109503
= 152030 cm
3
1 ℓ = 1000 cm
3 152030 cm
3 = 152.03 ℓ
Answer(s): (a) 282.012 ℓ; (b) 152.03 ℓ