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
34 filled with 116451 mℓ of water. The height of the water level in Container T is 4 cm higher than that in Container S. Height of Container T is 54 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 Container T in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container T = 116451 mℓ
14 of Container T = 116451 ÷ 3 = 38817 mℓ
44 of Container T = 38817 x 4 = 155268 mℓ
1 ℓ = 1000 mℓ
Capacity of Container T = 155268 mℓ = 155.268 ℓ
(b)
Fraction of Container T not filled
= 1 -
34 =
14 Height of Container T not filled
=
14 x 54 cm
= 13.5 cm
Height of Container S
= 54 - 13.5 - 4
= 36.5 cm
Volume of remaining water in Container S
= 36.5 x 36.5 x 36
= 47961 cm
3 Volume of remaining water in Container T
= 54 x 54 x 36
= 104976 cm
3 Total volume of remaining water in the container
= 47961 + 104976
= 152937 cm
3
1 ℓ = 1000 cm
3 152937 cm
3 = 152.937 ℓ
Answer(s): (a) 155.268 ℓ; (b) 152.937 ℓ