The figure, not drawn to scale, is made of two connected cubical tanks, A and B. Tank A is sealed at the top and completely filled to the brim. Tank B is
23 filled with 175838 mℓ of water. The height of the water level in Tank B is 5 cm higher than that in Tank A. Height of Tank B 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 B in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank B = 175838 mℓ
13 of Tank B = 175838 ÷ 2 = 87919 mℓ
33 of Tank B = 87919 x 3 = 263757 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank B = 263757 mℓ = 263.757 ℓ
(b)
Fraction of Tank B not filled
= 1 -
23 =
13 Height of Tank B not filled
=
13 x 66 cm
= 22 cm
Height of Tank A
= 66 - 22 - 5
= 39 cm
Volume of remaining water in Tank A
= 39 x 39 x 40
= 60840 cm
3 Volume of remaining water in Tank B
= 66 x 66 x 40
= 174240 cm
3 Total volume of remaining water in the tank
= 60840 + 174240
= 235080 cm
3
1 ℓ = 1000 cm
3 235080 cm
3 = 235.08 ℓ
Answer(s): (a) 263.757 ℓ; (b) 235.08 ℓ