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 104448 mℓ of water. The height of the water level in Tank V is 3 cm higher than that in Tank U. Height of Tank V is 58 cm. Water is then drained from the container and the height of the water level from the base falls to 20 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 = 104448 mℓ
14 of Tank V = 104448 ÷ 3 = 34816 mℓ
44 of Tank V = 34816 x 4 = 139264 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank V = 139264 mℓ = 139.264 ℓ
(b)
Fraction of Tank V not filled
= 1 -
34 =
14 Height of Tank V not filled
=
14 x 58 cm
= 14.5 cm
Height of Tank U
= 58 - 14.5 - 3
= 40.5 cm
Volume of remaining water in Tank U
= 40.5 x 40.5 x 20
= 32805 cm
3 Volume of remaining water in Tank V
= 58 x 58 x 20
= 67280 cm
3 Total volume of remaining water in the tank
= 32805 + 67280
= 100085 cm
3
1 ℓ = 1000 cm
3 100085 cm
3 = 100.085 ℓ
Answer(s): (a) 139.264 ℓ; (b) 100.085 ℓ