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
34 filled with 194874 mℓ of water. The height of the water level in Tank Z is 4 cm higher than that in Tank Y. Height of Tank Z is 70 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 Z in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank Z = 194874 mℓ
14 of Tank Z = 194874 ÷ 3 = 64958 mℓ
44 of Tank Z = 64958 x 4 = 259832 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank Z = 259832 mℓ = 259.832 ℓ
(b)
Fraction of Tank Z not filled
= 1 -
34 =
14 Height of Tank Z not filled
=
14 x 70 cm
= 17.5 cm
Height of Tank Y
= 70 - 17.5 - 4
= 48.5 cm
Volume of remaining water in Tank Y
= 48.5 x 48.5 x 20
= 47045 cm
3 Volume of remaining water in Tank Z
= 70 x 70 x 20
= 98000 cm
3 Total volume of remaining water in the tank
= 47045 + 98000
= 145045 cm
3
1 ℓ = 1000 cm
3 145045 cm
3 = 145.045 ℓ
Answer(s): (a) 259.832 ℓ; (b) 145.045 ℓ