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 150687 mℓ of water. The height of the water level in Tank J is 5 cm higher than that in Tank H. Height of Tank J is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 35 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 = 150687 mℓ
14 of Tank J = 150687 ÷ 3 = 50229 mℓ
44 of Tank J = 50229 x 4 = 200916 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank J = 200916 mℓ = 200.916 ℓ
(b)
Fraction of Tank J not filled
= 1 -
34 =
14 Height of Tank J not filled
=
14 x 68 cm
= 17 cm
Height of Tank H
= 68 - 17 - 5
= 46 cm
Volume of remaining water in Tank H
= 46 x 46 x 35
= 74060 cm
3 Volume of remaining water in Tank J
= 68 x 68 x 35
= 161840 cm
3 Total volume of remaining water in the tank
= 74060 + 161840
= 235900 cm
3
1 ℓ = 1000 cm
3 235900 cm
3 = 235.9 ℓ
Answer(s): (a) 200.916 ℓ; (b) 235.9 ℓ