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 196962 mℓ of water. The height of the water level in Container T is 1 cm higher than that in Container S. Height of Container T is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 25 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 = 196962 mℓ
15 of Container T = 196962 ÷ 3 = 65654 mℓ
55 of Container T = 65654 x 5 = 328270 mℓ
1 ℓ = 1000 mℓ
Capacity of Container T = 328270 mℓ = 328.27 ℓ
(b)
Fraction of Container T not filled
= 1 -
35 =
25 Height of Container T not filled
=
25 x 69 cm
= 27.6 cm
Height of Container S
= 69 - 27.6 - 1
= 40.4 cm
Volume of remaining water in Container S
= 40.4 x 40.4 x 25
= 40804 cm
3 Volume of remaining water in Container T
= 69 x 69 x 25
= 119025 cm
3 Total volume of remaining water in the container
= 40804 + 119025
= 159829 cm
3
1 ℓ = 1000 cm
3 159829 cm
3 = 159.829 ℓ
Answer(s): (a) 328.27 ℓ; (b) 159.829 ℓ