The figure, not drawn to scale, is made of two connected cubical tanks, Z and A. Tank Z is sealed at the top and completely filled to the brim. Tank A is
45 filled with 126528 mℓ of water. The height of the water level in Tank A is 5 cm higher than that in Tank Z. Height of Tank A is 70 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 A in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank A = 126528 mℓ
15 of Tank A = 126528 ÷ 4 = 31632 mℓ
55 of Tank A = 31632 x 5 = 158160 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank A = 158160 mℓ = 158.16 ℓ
(b)
Fraction of Tank A not filled
= 1 -
45 =
15 Height of Tank A not filled
=
15 x 70 cm
= 14 cm
Height of Tank Z
= 70 - 14 - 5
= 51 cm
Volume of remaining water in Tank Z
= 51 x 51 x 39
= 101439 cm
3 Volume of remaining water in Tank A
= 70 x 70 x 39
= 191100 cm
3 Total volume of remaining water in the tank
= 101439 + 191100
= 292539 cm
3
1 ℓ = 1000 cm
3 292539 cm
3 = 292.539 ℓ
Answer(s): (a) 158.16 ℓ; (b) 292.539 ℓ