The figure, not drawn to scale, is made of two connected cubical tanks, F and G. Tank F is sealed at the top and completely filled to the brim. Tank G is
34 filled with 193371 mℓ of water. The height of the water level in Tank G is 2 cm higher than that in Tank F. Height of Tank G is 64 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Tank G in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank G = 193371 mℓ
14 of Tank G = 193371 ÷ 3 = 64457 mℓ
44 of Tank G = 64457 x 4 = 257828 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank G = 257828 mℓ = 257.828 ℓ
(b)
Fraction of Tank G not filled
= 1 -
34 =
14 Height of Tank G not filled
=
14 x 64 cm
= 16 cm
Height of Tank F
= 64 - 16 - 2
= 46 cm
Volume of remaining water in Tank F
= 46 x 46 x 27
= 57132 cm
3 Volume of remaining water in Tank G
= 64 x 64 x 27
= 110592 cm
3 Total volume of remaining water in the tank
= 57132 + 110592
= 167724 cm
3
1 ℓ = 1000 cm
3 167724 cm
3 = 167.724 ℓ
Answer(s): (a) 257.828 ℓ; (b) 167.724 ℓ