The figure, not drawn to scale, is made of two connected cubical containers, H and J. Container H is sealed at the top and completely filled to the brim. Container J is
34 filled with 112911 mℓ of water. The height of the water level in Container J is 1 cm higher than that in Container H. Height of Container J is 62 cm. Water is then drained from the container and the height of the water level from the base falls to 24 cm.
- What is the capacity of Container J in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container J = 112911 mℓ
14 of Container J = 112911 ÷ 3 = 37637 mℓ
44 of Container J = 37637 x 4 = 150548 mℓ
1 ℓ = 1000 mℓ
Capacity of Container J = 150548 mℓ = 150.548 ℓ
(b)
Fraction of Container J not filled
= 1 -
34 =
14 Height of Container J not filled
=
14 x 62 cm
= 15.5 cm
Height of Container H
= 62 - 15.5 - 1
= 45.5 cm
Volume of remaining water in Container H
= 45.5 x 45.5 x 24
= 49686 cm
3 Volume of remaining water in Container J
= 62 x 62 x 24
= 92256 cm
3 Total volume of remaining water in the container
= 49686 + 92256
= 141942 cm
3
1 ℓ = 1000 cm
3 141942 cm
3 = 141.942 ℓ
Answer(s): (a) 150.548 ℓ; (b) 141.942 ℓ