The figure, not drawn to scale, is made of two connected cubical containers, Z and A. Container Z is sealed at the top and completely filled to the brim. Container A is
35 filled with 176712 mℓ of water. The height of the water level in Container A is 4 cm higher than that in Container Z. Height of Container A is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 30 cm.
- What is the capacity of Container A in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container A = 176712 mℓ
15 of Container A = 176712 ÷ 3 = 58904 mℓ
55 of Container A = 58904 x 5 = 294520 mℓ
1 ℓ = 1000 mℓ
Capacity of Container A = 294520 mℓ = 294.52 ℓ
(b)
Fraction of Container A not filled
= 1 -
35 =
25 Height of Container A not filled
=
25 x 70 cm
= 28 cm
Height of Container Z
= 70 - 28 - 4
= 38 cm
Volume of remaining water in Container Z
= 38 x 38 x 30
= 43320 cm
3 Volume of remaining water in Container A
= 70 x 70 x 30
= 147000 cm
3 Total volume of remaining water in the container
= 43320 + 147000
= 190320 cm
3
1 ℓ = 1000 cm
3 190320 cm
3 = 190.32 ℓ
Answer(s): (a) 294.52 ℓ; (b) 190.32 ℓ