The figure, not drawn to scale, is made of two connected cubical tanks, H and J. Tank H is sealed at the top and completely filled to the brim. Tank J is
34 filled with 111027 mℓ of water. The height of the water level in Tank J is 2 cm higher than that in Tank H. Height of Tank J is 53 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Tank J in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank J = 111027 mℓ
14 of Tank J = 111027 ÷ 3 = 37009 mℓ
44 of Tank J = 37009 x 4 = 148036 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank J = 148036 mℓ = 148.036 ℓ
(b)
Fraction of Tank J not filled
= 1 -
34 =
14 Height of Tank J not filled
=
14 x 53 cm
= 13.25 cm
Height of Tank H
= 53 - 13.25 - 2
= 37.75 cm
Volume of remaining water in Tank H
= 37.75 x 37.75 x 32
= 45602 cm
3 Volume of remaining water in Tank J
= 53 x 53 x 32
= 89888 cm
3 Total volume of remaining water in the tank
= 45602 + 89888
= 135490 cm
3
1 ℓ = 1000 cm
3 135490 cm
3 = 135.49 ℓ
Answer(s): (a) 148.036 ℓ; (b) 135.49 ℓ