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 122964 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 64 cm. Water is then drained from the container and the height of the water level from the base falls to 28 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 = 122964 mℓ
14 of Tank J = 122964 ÷ 3 = 40988 mℓ
44 of Tank J = 40988 x 4 = 163952 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank J = 163952 mℓ = 163.952 ℓ
(b)
Fraction of Tank J not filled
= 1 -
34 =
14 Height of Tank J not filled
=
14 x 64 cm
= 16 cm
Height of Tank H
= 64 - 16 - 5
= 43 cm
Volume of remaining water in Tank H
= 43 x 43 x 28
= 51772 cm
3 Volume of remaining water in Tank J
= 64 x 64 x 28
= 114688 cm
3 Total volume of remaining water in the tank
= 51772 + 114688
= 166460 cm
3
1 ℓ = 1000 cm
3 166460 cm
3 = 166.46 ℓ
Answer(s): (a) 163.952 ℓ; (b) 166.46 ℓ