The figure, not drawn to scale, is made of two connected cubical containers, S and T. Container S is sealed at the top and completely filled to the brim. Container T is
23 filled with 104606 mℓ of water. The height of the water level in Container T is 5 cm higher than that in Container S. Height of Container T is 57 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Container T in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container T = 104606 mℓ
13 of Container T = 104606 ÷ 2 = 52303 mℓ
33 of Container T = 52303 x 3 = 156909 mℓ
1 ℓ = 1000 mℓ
Capacity of Container T = 156909 mℓ = 156.909 ℓ
(b)
Fraction of Container T not filled
= 1 -
23 =
13 Height of Container T not filled
=
13 x 57 cm
= 19 cm
Height of Container S
= 57 - 19 - 5
= 33 cm
Volume of remaining water in Container S
= 33 x 33 x 27
= 29403 cm
3 Volume of remaining water in Container T
= 57 x 57 x 27
= 87723 cm
3 Total volume of remaining water in the container
= 29403 + 87723
= 117126 cm
3
1 ℓ = 1000 cm
3 117126 cm
3 = 117.126 ℓ
Answer(s): (a) 156.909 ℓ; (b) 117.126 ℓ