The figure, not drawn to scale, is made of two connected cubical tanks, Z and A. Tank Z is sealed at the top and completely filled to the brim. Tank A is
34 filled with 110187 mℓ of water. The height of the water level in Tank A is 4 cm higher than that in Tank Z. Height of Tank A is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 28 cm.
- What is the capacity of Tank A in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank A = 110187 mℓ
14 of Tank A = 110187 ÷ 3 = 36729 mℓ
44 of Tank A = 36729 x 4 = 146916 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank A = 146916 mℓ = 146.916 ℓ
(b)
Fraction of Tank A not filled
= 1 -
34 =
14 Height of Tank A not filled
=
14 x 70 cm
= 17.5 cm
Height of Tank Z
= 70 - 17.5 - 4
= 48.5 cm
Volume of remaining water in Tank Z
= 48.5 x 48.5 x 28
= 65863 cm
3 Volume of remaining water in Tank A
= 70 x 70 x 28
= 137200 cm
3 Total volume of remaining water in the tank
= 65863 + 137200
= 203063 cm
3
1 ℓ = 1000 cm
3 203063 cm
3 = 203.063 ℓ
Answer(s): (a) 146.916 ℓ; (b) 203.063 ℓ