The figure, not drawn to scale, is made of two connected cubical tanks, C and D. Tank C is sealed at the top and completely filled to the brim. Tank D is
23 filled with 102908 mℓ of water. The height of the water level in Tank D is 4 cm higher than that in Tank C. Height of Tank D is 57 cm. Water is then drained from the container and the height of the water level from the base falls to 35 cm.
- What is the capacity of Tank D in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank D = 102908 mℓ
13 of Tank D = 102908 ÷ 2 = 51454 mℓ
33 of Tank D = 51454 x 3 = 154362 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank D = 154362 mℓ = 154.362 ℓ
(b)
Fraction of Tank D not filled
= 1 -
23 =
13 Height of Tank D not filled
=
13 x 57 cm
= 19 cm
Height of Tank C
= 57 - 19 - 4
= 34 cm
Volume of remaining water in Tank C
= 34 x 34 x 35
= 40460 cm
3 Volume of remaining water in Tank D
= 57 x 57 x 35
= 113715 cm
3 Total volume of remaining water in the tank
= 40460 + 113715
= 154175 cm
3
1 ℓ = 1000 cm
3 154175 cm
3 = 154.175 ℓ
Answer(s): (a) 154.362 ℓ; (b) 154.175 ℓ