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
23 filled with 137620 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 60 cm. Water is then drained from the container and the height of the water level from the base falls to 23 cm.
- What is the capacity of Tank J in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank J = 137620 mℓ
13 of Tank J = 137620 ÷ 2 = 68810 mℓ
33 of Tank J = 68810 x 3 = 206430 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank J = 206430 mℓ = 206.43 ℓ
(b)
Fraction of Tank J not filled
= 1 -
23 =
13 Height of Tank J not filled
=
13 x 60 cm
= 20 cm
Height of Tank H
= 60 - 20 - 2
= 38 cm
Volume of remaining water in Tank H
= 38 x 38 x 23
= 33212 cm
3 Volume of remaining water in Tank J
= 60 x 60 x 23
= 82800 cm
3 Total volume of remaining water in the tank
= 33212 + 82800
= 116012 cm
3
1 ℓ = 1000 cm
3 116012 cm
3 = 116.012 ℓ
Answer(s): (a) 206.43 ℓ; (b) 116.012 ℓ