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
23 filled with 117080 mℓ of water. The height of the water level in Tank U is 5 cm higher than that in Tank T. Height of Tank U is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 23 cm.
- What is the capacity of Tank U in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank U = 117080 mℓ
13 of Tank U = 117080 ÷ 2 = 58540 mℓ
33 of Tank U = 58540 x 3 = 175620 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank U = 175620 mℓ = 175.62 ℓ
(b)
Fraction of Tank U not filled
= 1 -
23 =
13 Height of Tank U not filled
=
13 x 69 cm
= 23 cm
Height of Tank T
= 69 - 23 - 5
= 41 cm
Volume of remaining water in Tank T
= 41 x 41 x 23
= 38663 cm
3 Volume of remaining water in Tank U
= 69 x 69 x 23
= 109503 cm
3 Total volume of remaining water in the tank
= 38663 + 109503
= 148166 cm
3
1 ℓ = 1000 cm
3 148166 cm
3 = 148.166 ℓ
Answer(s): (a) 175.62 ℓ; (b) 148.166 ℓ