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 145948 mℓ of water. The height of the water level in Tank U is 4 cm higher than that in Tank T. Height of Tank U is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 27 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 = 145948 mℓ
13 of Tank U = 145948 ÷ 2 = 72974 mℓ
33 of Tank U = 72974 x 3 = 218922 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank U = 218922 mℓ = 218.922 ℓ
(b)
Fraction of Tank U not filled
= 1 -
23 =
13 Height of Tank U not filled
=
13 x 63 cm
= 21 cm
Height of Tank T
= 63 - 21 - 4
= 38 cm
Volume of remaining water in Tank T
= 38 x 38 x 27
= 38988 cm
3 Volume of remaining water in Tank U
= 63 x 63 x 27
= 107163 cm
3 Total volume of remaining water in the tank
= 38988 + 107163
= 146151 cm
3
1 ℓ = 1000 cm
3 146151 cm
3 = 146.151 ℓ
Answer(s): (a) 218.922 ℓ; (b) 146.151 ℓ