The figure, not drawn to scale, is made of two connected cubical containers, R and S. Container R is sealed at the top and completely filled to the brim. Container S is
23 filled with 100982 mℓ of water. The height of the water level in Container S is 4 cm higher than that in Container R. Height of Container S is 54 cm. Water is then drained from the container and the height of the water level from the base falls to 24 cm.
- What is the capacity of Container S in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container S = 100982 mℓ
13 of Container S = 100982 ÷ 2 = 50491 mℓ
33 of Container S = 50491 x 3 = 151473 mℓ
1 ℓ = 1000 mℓ
Capacity of Container S = 151473 mℓ = 151.473 ℓ
(b)
Fraction of Container S not filled
= 1 -
23 =
13 Height of Container S not filled
=
13 x 54 cm
= 18 cm
Height of Container R
= 54 - 18 - 4
= 32 cm
Volume of remaining water in Container R
= 32 x 32 x 24
= 24576 cm
3 Volume of remaining water in Container S
= 54 x 54 x 24
= 69984 cm
3 Total volume of remaining water in the container
= 24576 + 69984
= 94560 cm
3
1 ℓ = 1000 cm
3 94560 cm
3 = 94.56 ℓ
Answer(s): (a) 151.473 ℓ; (b) 94.56 ℓ