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 138160 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 25 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 = 138160 mℓ
13 of Tank Y = 138160 ÷ 2 = 69080 mℓ
33 of Tank Y = 69080 x 3 = 207240 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Y = 207240 mℓ = 207.24 ℓ
(b)
Fraction of Tank Y not filled
= 1 -
23 =
13 Height of Tank Y not filled
=
13 x 66 cm
= 22 cm
Height of Tank X
= 66 - 22 - 1
= 43 cm
Volume of remaining water in Tank X
= 43 x 43 x 25
= 46225 cm
3 Volume of remaining water in Tank Y
= 66 x 66 x 25
= 108900 cm
3 Total volume of remaining water in the tank
= 46225 + 108900
= 155125 cm
3
1 ℓ = 1000 cm
3 155125 cm
3 = 155.125 ℓ
Answer(s): (a) 207.24 ℓ; (b) 155.125 ℓ