The figure, not drawn to scale, is made of two connected cubical tanks, V and W. Tank V is sealed at the top and completely filled to the brim. Tank W is
45 filled with 171828 mℓ of water. The height of the water level in Tank W is 3 cm higher than that in Tank V. Height of Tank W is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Tank W in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank W = 171828 mℓ
15 of Tank W = 171828 ÷ 4 = 42957 mℓ
55 of Tank W = 42957 x 5 = 214785 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank W = 214785 mℓ = 214.785 ℓ
(b)
Fraction of Tank W not filled
= 1 -
45 =
15 Height of Tank W not filled
=
15 x 60 cm
= 12 cm
Height of Tank V
= 60 - 12 - 3
= 45 cm
Volume of remaining water in Tank V
= 45 x 45 x 31
= 62775 cm
3 Volume of remaining water in Tank W
= 60 x 60 x 31
= 111600 cm
3 Total volume of remaining water in the tank
= 62775 + 111600
= 174375 cm
3
1 ℓ = 1000 cm
3 174375 cm
3 = 174.375 ℓ
Answer(s): (a) 214.785 ℓ; (b) 174.375 ℓ