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
45 filled with 184848 mℓ of water. The height of the water level in Tank V is 2 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 29 cm.
- What is the capacity of Tank V in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank V = 184848 mℓ
15 of Tank V = 184848 ÷ 4 = 46212 mℓ
55 of Tank V = 46212 x 5 = 231060 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank V = 231060 mℓ = 231.06 ℓ
(b)
Fraction of Tank V not filled
= 1 -
45 =
15 Height of Tank V not filled
=
15 x 65 cm
= 13 cm
Height of Tank U
= 65 - 13 - 2
= 50 cm
Volume of remaining water in Tank U
= 50 x 50 x 29
= 72500 cm
3 Volume of remaining water in Tank V
= 65 x 65 x 29
= 122525 cm
3 Total volume of remaining water in the tank
= 72500 + 122525
= 195025 cm
3
1 ℓ = 1000 cm
3 195025 cm
3 = 195.025 ℓ
Answer(s): (a) 231.06 ℓ; (b) 195.025 ℓ