The figure, not drawn to scale, is made of two connected cubical tanks, S and T. Tank S is sealed at the top and completely filled to the brim. Tank T is
23 filled with 191272 mℓ of water. The height of the water level in Tank T is 4 cm higher than that in Tank S. Height of Tank T is 66 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 T in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank T = 191272 mℓ
13 of Tank T = 191272 ÷ 2 = 95636 mℓ
33 of Tank T = 95636 x 3 = 286908 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank T = 286908 mℓ = 286.908 ℓ
(b)
Fraction of Tank T not filled
= 1 -
23 =
13 Height of Tank T not filled
=
13 x 66 cm
= 22 cm
Height of Tank S
= 66 - 22 - 4
= 40 cm
Volume of remaining water in Tank S
= 40 x 40 x 38
= 60800 cm
3 Volume of remaining water in Tank T
= 66 x 66 x 38
= 165528 cm
3 Total volume of remaining water in the tank
= 60800 + 165528
= 226328 cm
3
1 ℓ = 1000 cm
3 226328 cm
3 = 226.328 ℓ
Answer(s): (a) 286.908 ℓ; (b) 226.328 ℓ