The figure, not drawn to scale, is made of two connected cubical containers, U and V. Container U is sealed at the top and completely filled to the brim. Container V is
34 filled with 117141 mℓ of water. The height of the water level in Container V is 1 cm higher than that in Container U. Height of Container V is 59 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 V in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container V = 117141 mℓ
14 of Container V = 117141 ÷ 3 = 39047 mℓ
44 of Container V = 39047 x 4 = 156188 mℓ
1 ℓ = 1000 mℓ
Capacity of Container V = 156188 mℓ = 156.188 ℓ
(b)
Fraction of Container V not filled
= 1 -
34 =
14 Height of Container V not filled
=
14 x 59 cm
= 14.75 cm
Height of Container U
= 59 - 14.75 - 1
= 43.25 cm
Volume of remaining water in Container U
= 43.25 x 43.25 x 32
= 59858 cm
3 Volume of remaining water in Container V
= 59 x 59 x 32
= 111392 cm
3 Total volume of remaining water in the container
= 59858 + 111392
= 171250 cm
3
1 ℓ = 1000 cm
3 171250 cm
3 = 171.25 ℓ
Answer(s): (a) 156.188 ℓ; (b) 171.25 ℓ