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
35 filled with 137814 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 70 cm. Water is then drained from the container and the height of the water level from the base falls to 38 cm.
- What is the capacity of Tank G in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank G = 137814 mℓ
15 of Tank G = 137814 ÷ 3 = 45938 mℓ
55 of Tank G = 45938 x 5 = 229690 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank G = 229690 mℓ = 229.69 ℓ
(b)
Fraction of Tank G not filled
= 1 -
35 =
25 Height of Tank G not filled
=
25 x 70 cm
= 28 cm
Height of Tank F
= 70 - 28 - 2
= 40 cm
Volume of remaining water in Tank F
= 40 x 40 x 38
= 60800 cm
3 Volume of remaining water in Tank G
= 70 x 70 x 38
= 186200 cm
3 Total volume of remaining water in the tank
= 60800 + 186200
= 247000 cm
3
1 ℓ = 1000 cm
3 247000 cm
3 = 247 ℓ
Answer(s): (a) 229.69 ℓ; (b) 247 ℓ