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
35 filled with 133296 mℓ of water. The height of the water level in Tank V is 5 cm higher than that in Tank U. Height of Tank V is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Tank V in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank V = 133296 mℓ
15 of Tank V = 133296 ÷ 3 = 44432 mℓ
55 of Tank V = 44432 x 5 = 222160 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank V = 222160 mℓ = 222.16 ℓ
(b)
Fraction of Tank V not filled
= 1 -
35 =
25 Height of Tank V not filled
=
25 x 70 cm
= 28 cm
Height of Tank U
= 70 - 28 - 5
= 37 cm
Volume of remaining water in Tank U
= 37 x 37 x 40
= 54760 cm
3 Volume of remaining water in Tank V
= 70 x 70 x 40
= 196000 cm
3 Total volume of remaining water in the tank
= 54760 + 196000
= 250760 cm
3
1 ℓ = 1000 cm
3 250760 cm
3 = 250.76 ℓ
Answer(s): (a) 222.16 ℓ; (b) 250.76 ℓ