The figure, not drawn to scale, is made of two connected cubical containers, C and D. Container C is sealed at the top and completely filled to the brim. Container D is
23 filled with 143636 mℓ of water. The height of the water level in Container D is 5 cm higher than that in Container C. Height of Container D is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.
- What is the capacity of Container D in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container D = 143636 mℓ
13 of Container D = 143636 ÷ 2 = 71818 mℓ
33 of Container D = 71818 x 3 = 215454 mℓ
1 ℓ = 1000 mℓ
Capacity of Container D = 215454 mℓ = 215.454 ℓ
(b)
Fraction of Container D not filled
= 1 -
23 =
13 Height of Container D not filled
=
13 x 60 cm
= 20 cm
Height of Container C
= 60 - 20 - 5
= 35 cm
Volume of remaining water in Container C
= 35 x 35 x 34
= 41650 cm
3 Volume of remaining water in Container D
= 60 x 60 x 34
= 122400 cm
3 Total volume of remaining water in the container
= 41650 + 122400
= 164050 cm
3
1 ℓ = 1000 cm
3 164050 cm
3 = 164.05 ℓ
Answer(s): (a) 215.454 ℓ; (b) 164.05 ℓ