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 103884 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 56 cm. Water is then drained from the container and the height of the water level from the base falls to 21 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 = 103884 mℓ
14 of Tank V = 103884 ÷ 3 = 34628 mℓ
44 of Tank V = 34628 x 4 = 138512 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank V = 138512 mℓ = 138.512 ℓ
(b)
Fraction of Tank V not filled
= 1 -
34 =
14 Height of Tank V not filled
=
14 x 56 cm
= 14 cm
Height of Tank U
= 56 - 14 - 4
= 38 cm
Volume of remaining water in Tank U
= 38 x 38 x 21
= 30324 cm
3 Volume of remaining water in Tank V
= 56 x 56 x 21
= 65856 cm
3 Total volume of remaining water in the tank
= 30324 + 65856
= 96180 cm
3
1 ℓ = 1000 cm
3 96180 cm
3 = 96.18 ℓ
Answer(s): (a) 138.512 ℓ; (b) 96.18 ℓ