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
34 filled with 196521 mℓ of water. The height of the water level in Container S is 2 cm higher than that in Container R. Height of Container S is 66 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 S in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container S = 196521 mℓ
14 of Container S = 196521 ÷ 3 = 65507 mℓ
44 of Container S = 65507 x 4 = 262028 mℓ
1 ℓ = 1000 mℓ
Capacity of Container S = 262028 mℓ = 262.028 ℓ
(b)
Fraction of Container S not filled
= 1 -
34 =
14 Height of Container S not filled
=
14 x 66 cm
= 16.5 cm
Height of Container R
= 66 - 16.5 - 2
= 47.5 cm
Volume of remaining water in Container R
= 47.5 x 47.5 x 36
= 81225 cm
3 Volume of remaining water in Container S
= 66 x 66 x 36
= 156816 cm
3 Total volume of remaining water in the container
= 81225 + 156816
= 238041 cm
3
1 ℓ = 1000 cm
3 238041 cm
3 = 238.041 ℓ
Answer(s): (a) 262.028 ℓ; (b) 238.041 ℓ