The figure, not drawn to scale, is made of two connected cubical tanks, G and H. Tank G is sealed at the top and completely filled to the brim. Tank H is
34 filled with 120009 mℓ of water. The height of the water level in Tank H is 4 cm higher than that in Tank G. Height of Tank H is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Tank H in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank H = 120009 mℓ
14 of Tank H = 120009 ÷ 3 = 40003 mℓ
44 of Tank H = 40003 x 4 = 160012 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank H = 160012 mℓ = 160.012 ℓ
(b)
Fraction of Tank H not filled
= 1 -
34 =
14 Height of Tank H not filled
=
14 x 66 cm
= 16.5 cm
Height of Tank G
= 66 - 16.5 - 4
= 45.5 cm
Volume of remaining water in Tank G
= 45.5 x 45.5 x 40
= 82810 cm
3 Volume of remaining water in Tank H
= 66 x 66 x 40
= 174240 cm
3 Total volume of remaining water in the tank
= 82810 + 174240
= 257050 cm
3
1 ℓ = 1000 cm
3 257050 cm
3 = 257.05 ℓ
Answer(s): (a) 160.012 ℓ; (b) 257.05 ℓ