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 121404 mℓ of water. The height of the water level in Tank A is 5 cm higher than that in Tank Z. Height of Tank A is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 39 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 = 121404 mℓ
14 of Tank A = 121404 ÷ 3 = 40468 mℓ
44 of Tank A = 40468 x 4 = 161872 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank A = 161872 mℓ = 161.872 ℓ
(b)
Fraction of Tank A not filled
= 1 -
34 =
14 Height of Tank A not filled
=
14 x 68 cm
= 17 cm
Height of Tank Z
= 68 - 17 - 5
= 46 cm
Volume of remaining water in Tank Z
= 46 x 46 x 39
= 82524 cm
3 Volume of remaining water in Tank A
= 68 x 68 x 39
= 180336 cm
3 Total volume of remaining water in the tank
= 82524 + 180336
= 262860 cm
3
1 ℓ = 1000 cm
3 262860 cm
3 = 262.86 ℓ
Answer(s): (a) 161.872 ℓ; (b) 262.86 ℓ