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
23 filled with 118500 mℓ of water. The height of the water level in Tank G is 1 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 36 cm.
- What is the capacity of Tank G in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank G = 118500 mℓ
13 of Tank G = 118500 ÷ 2 = 59250 mℓ
33 of Tank G = 59250 x 3 = 177750 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank G = 177750 mℓ = 177.75 ℓ
(b)
Fraction of Tank G not filled
= 1 -
23 =
13 Height of Tank G not filled
=
13 x 70 cm
= 23.333333333333 cm
Height of Tank F
= 70 - 23.333333333333 - 1
= 45.666666666667 cm
Volume of remaining water in Tank F
= 45.666666666667 x 45.666666666667 x 36
= 75076.000000001 cm
3 Volume of remaining water in Tank G
= 70 x 70 x 36
= 176400 cm
3 Total volume of remaining water in the tank
= 75076.000000001 + 176400
= 251476 cm
3
1 ℓ = 1000 cm
3 251476 cm
3 = 251.476 ℓ
Answer(s): (a) 177.75 ℓ; (b) 251.476 ℓ