The figure, not drawn to scale, is made of two connected cubical tanks, W and X. Tank W is sealed at the top and completely filled to the brim. Tank X is
23 filled with 135874 mℓ of water. The height of the water level in Tank X is 4 cm higher than that in Tank W. Height of Tank X is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 33 cm.
- What is the capacity of Tank X in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank X = 135874 mℓ
13 of Tank X = 135874 ÷ 2 = 67937 mℓ
33 of Tank X = 67937 x 3 = 203811 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank X = 203811 mℓ = 203.811 ℓ
(b)
Fraction of Tank X not filled
= 1 -
23 =
13 Height of Tank X not filled
=
13 x 63 cm
= 21 cm
Height of Tank W
= 63 - 21 - 4
= 38 cm
Volume of remaining water in Tank W
= 38 x 38 x 33
= 47652 cm
3 Volume of remaining water in Tank X
= 63 x 63 x 33
= 130977 cm
3 Total volume of remaining water in the tank
= 47652 + 130977
= 178629 cm
3
1 ℓ = 1000 cm
3 178629 cm
3 = 178.629 ℓ
Answer(s): (a) 203.811 ℓ; (b) 178.629 ℓ