The figure, not drawn to scale, is made of two connected cubical tanks, V and W. Tank V is sealed at the top and completely filled to the brim. Tank W is
35 filled with 153420 mℓ of water. The height of the water level in Tank W is 2 cm higher than that in Tank V. Height of Tank W is 70 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 W in litres?
- What is the volume of water in the tank now in litres?
(a)
35 of Tank W = 153420 mℓ
15 of Tank W = 153420 ÷ 3 = 51140 mℓ
55 of Tank W = 51140 x 5 = 255700 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank W = 255700 mℓ = 255.7 ℓ
(b)
Fraction of Tank W not filled
= 1 -
35 =
25 Height of Tank W not filled
=
25 x 70 cm
= 28 cm
Height of Tank V
= 70 - 28 - 2
= 40 cm
Volume of remaining water in Tank V
= 40 x 40 x 21
= 33600 cm
3 Volume of remaining water in Tank W
= 70 x 70 x 21
= 102900 cm
3 Total volume of remaining water in the tank
= 33600 + 102900
= 136500 cm
3
1 ℓ = 1000 cm
3 136500 cm
3 = 136.5 ℓ
Answer(s): (a) 255.7 ℓ; (b) 136.5 ℓ