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 108207 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 65 cm. Water is then drained from the container and the height of the water level from the base falls to 24 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 = 108207 mℓ
15 of Tank V = 108207 ÷ 3 = 36069 mℓ
55 of Tank V = 36069 x 5 = 180345 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank V = 180345 mℓ = 180.345 ℓ
(b)
Fraction of Tank V not filled
= 1 -
35 =
25 Height of Tank V not filled
=
25 x 65 cm
= 26 cm
Height of Tank U
= 65 - 26 - 5
= 34 cm
Volume of remaining water in Tank U
= 34 x 34 x 24
= 27744 cm
3 Volume of remaining water in Tank V
= 65 x 65 x 24
= 101400 cm
3 Total volume of remaining water in the tank
= 27744 + 101400
= 129144 cm
3
1 ℓ = 1000 cm
3 129144 cm
3 = 129.144 ℓ
Answer(s): (a) 180.345 ℓ; (b) 129.144 ℓ