The figure, not drawn to scale, is made of two connected cubical tanks, T and U. Tank T is sealed at the top and completely filled to the brim. Tank U is
45 filled with 170296 mℓ of water. The height of the water level in Tank U is 3 cm higher than that in Tank T. Height of Tank U is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 33 cm.
- What is the capacity of Tank U in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank U = 170296 mℓ
15 of Tank U = 170296 ÷ 4 = 42574 mℓ
55 of Tank U = 42574 x 5 = 212870 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank U = 212870 mℓ = 212.87 ℓ
(b)
Fraction of Tank U not filled
= 1 -
45 =
15 Height of Tank U not filled
=
15 x 60 cm
= 12 cm
Height of Tank T
= 60 - 12 - 3
= 45 cm
Volume of remaining water in Tank T
= 45 x 45 x 33
= 66825 cm
3 Volume of remaining water in Tank U
= 60 x 60 x 33
= 118800 cm
3 Total volume of remaining water in the tank
= 66825 + 118800
= 185625 cm
3
1 ℓ = 1000 cm
3 185625 cm
3 = 185.625 ℓ
Answer(s): (a) 212.87 ℓ; (b) 185.625 ℓ