The figure, not drawn to scale, is made of two connected cubical tanks, U and V. Tank U is sealed at the top and completely filled to the brim. Tank V is
34 filled with 187815 mℓ of water. The height of the water level in Tank V is 4 cm higher than that in Tank U. Height of Tank V is 64 cm. Water is then drained from the container and the height of the water level from the base falls to 26 cm.
- What is the capacity of Tank V in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank V = 187815 mℓ
14 of Tank V = 187815 ÷ 3 = 62605 mℓ
44 of Tank V = 62605 x 4 = 250420 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank V = 250420 mℓ = 250.42 ℓ
(b)
Fraction of Tank V not filled
= 1 -
34 =
14 Height of Tank V not filled
=
14 x 64 cm
= 16 cm
Height of Tank U
= 64 - 16 - 4
= 44 cm
Volume of remaining water in Tank U
= 44 x 44 x 26
= 50336 cm
3 Volume of remaining water in Tank V
= 64 x 64 x 26
= 106496 cm
3 Total volume of remaining water in the tank
= 50336 + 106496
= 156832 cm
3
1 ℓ = 1000 cm
3 156832 cm
3 = 156.832 ℓ
Answer(s): (a) 250.42 ℓ; (b) 156.832 ℓ