The figure, not drawn to scale, is made of two connected cubical tanks, B and C. Tank B is sealed at the top and completely filled to the brim. Tank C is
23 filled with 191514 mℓ of water. The height of the water level in Tank C is 2 cm higher than that in Tank B. Height of Tank C is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 39 cm.
- What is the capacity of Tank C in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank C = 191514 mℓ
13 of Tank C = 191514 ÷ 2 = 95757 mℓ
33 of Tank C = 95757 x 3 = 287271 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank C = 287271 mℓ = 287.271 ℓ
(b)
Fraction of Tank C not filled
= 1 -
23 =
13 Height of Tank C not filled
=
13 x 66 cm
= 22 cm
Height of Tank B
= 66 - 22 - 2
= 42 cm
Volume of remaining water in Tank B
= 42 x 42 x 39
= 68796 cm
3 Volume of remaining water in Tank C
= 66 x 66 x 39
= 169884 cm
3 Total volume of remaining water in the tank
= 68796 + 169884
= 238680 cm
3
1 ℓ = 1000 cm
3 238680 cm
3 = 238.68 ℓ
Answer(s): (a) 287.271 ℓ; (b) 238.68 ℓ