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 148806 mℓ of water. The height of the water level in Tank Y is 2 cm higher than that in Tank X. Height of Tank Y is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 20 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 = 148806 mℓ
14 of Tank Y = 148806 ÷ 3 = 49602 mℓ
44 of Tank Y = 49602 x 4 = 198408 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Y = 198408 mℓ = 198.408 ℓ
(b)
Fraction of Tank Y not filled
= 1 -
34 =
14 Height of Tank Y not filled
=
14 x 68 cm
= 17 cm
Height of Tank X
= 68 - 17 - 2
= 49 cm
Volume of remaining water in Tank X
= 49 x 49 x 20
= 48020 cm
3 Volume of remaining water in Tank Y
= 68 x 68 x 20
= 92480 cm
3 Total volume of remaining water in the tank
= 48020 + 92480
= 140500 cm
3
1 ℓ = 1000 cm
3 140500 cm
3 = 140.5 ℓ
Answer(s): (a) 198.408 ℓ; (b) 140.5 ℓ