The figure, not drawn to scale, is made of two connected cubical tanks, W and X. Tank W is sealed at the top and completely filled to the brim. Tank X is
23 filled with 121540 mℓ of water. The height of the water level in Tank X is 3 cm higher than that in Tank W. Height of Tank X is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Tank X in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank X = 121540 mℓ
13 of Tank X = 121540 ÷ 2 = 60770 mℓ
33 of Tank X = 60770 x 3 = 182310 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank X = 182310 mℓ = 182.31 ℓ
(b)
Fraction of Tank X not filled
= 1 -
23 =
13 Height of Tank X not filled
=
13 x 69 cm
= 23 cm
Height of Tank W
= 69 - 23 - 3
= 43 cm
Volume of remaining water in Tank W
= 43 x 43 x 40
= 73960 cm
3 Volume of remaining water in Tank X
= 69 x 69 x 40
= 190440 cm
3 Total volume of remaining water in the tank
= 73960 + 190440
= 264400 cm
3
1 ℓ = 1000 cm
3 264400 cm
3 = 264.4 ℓ
Answer(s): (a) 182.31 ℓ; (b) 264.4 ℓ