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
34 filled with 113907 mℓ of water. The height of the water level in Tank A is 3 cm higher than that in Tank Z. Height of Tank A is 56 cm. Water is then drained from the container and the height of the water level from the base falls to 36 cm.
- What is the capacity of Tank A in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank A = 113907 mℓ
14 of Tank A = 113907 ÷ 3 = 37969 mℓ
44 of Tank A = 37969 x 4 = 151876 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank A = 151876 mℓ = 151.876 ℓ
(b)
Fraction of Tank A not filled
= 1 -
34 =
14 Height of Tank A not filled
=
14 x 56 cm
= 14 cm
Height of Tank Z
= 56 - 14 - 3
= 39 cm
Volume of remaining water in Tank Z
= 39 x 39 x 36
= 54756 cm
3 Volume of remaining water in Tank A
= 56 x 56 x 36
= 112896 cm
3 Total volume of remaining water in the tank
= 54756 + 112896
= 167652 cm
3
1 ℓ = 1000 cm
3 167652 cm
3 = 167.652 ℓ
Answer(s): (a) 151.876 ℓ; (b) 167.652 ℓ