The figure, not drawn to scale, is made of two connected cubical containers, E and F. Container E is sealed at the top and completely filled to the brim. Container F is
34 filled with 124398 mℓ of water. The height of the water level in Container F is 1 cm higher than that in Container E. Height of Container F is 62 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Container F in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container F = 124398 mℓ
14 of Container F = 124398 ÷ 3 = 41466 mℓ
44 of Container F = 41466 x 4 = 165864 mℓ
1 ℓ = 1000 mℓ
Capacity of Container F = 165864 mℓ = 165.864 ℓ
(b)
Fraction of Container F not filled
= 1 -
34 =
14 Height of Container F not filled
=
14 x 62 cm
= 15.5 cm
Height of Container E
= 62 - 15.5 - 1
= 45.5 cm
Volume of remaining water in Container E
= 45.5 x 45.5 x 32
= 66248 cm
3 Volume of remaining water in Container F
= 62 x 62 x 32
= 123008 cm
3 Total volume of remaining water in the container
= 66248 + 123008
= 189256 cm
3
1 ℓ = 1000 cm
3 189256 cm
3 = 189.256 ℓ
Answer(s): (a) 165.864 ℓ; (b) 189.256 ℓ