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
35 filled with 116409 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 60 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Container T in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container T = 116409 mℓ
15 of Container T = 116409 ÷ 3 = 38803 mℓ
55 of Container T = 38803 x 5 = 194015 mℓ
1 ℓ = 1000 mℓ
Capacity of Container T = 194015 mℓ = 194.015 ℓ
(b)
Fraction of Container T not filled
= 1 -
35 =
25 Height of Container T not filled
=
25 x 60 cm
= 24 cm
Height of Container S
= 60 - 24 - 5
= 31 cm
Volume of remaining water in Container S
= 31 x 31 x 32
= 30752 cm
3 Volume of remaining water in Container T
= 60 x 60 x 32
= 115200 cm
3 Total volume of remaining water in the container
= 30752 + 115200
= 145952 cm
3
1 ℓ = 1000 cm
3 145952 cm
3 = 145.952 ℓ
Answer(s): (a) 194.015 ℓ; (b) 145.952 ℓ