The figure, not drawn to scale, is made of two connected cubical tanks, E and F. Tank E is sealed at the top and completely filled to the brim. Tank F is
23 filled with 109624 mℓ of water. The height of the water level in Tank F is 5 cm higher than that in Tank E. Height of Tank F is 57 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 F in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank F = 109624 mℓ
13 of Tank F = 109624 ÷ 2 = 54812 mℓ
33 of Tank F = 54812 x 3 = 164436 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank F = 164436 mℓ = 164.436 ℓ
(b)
Fraction of Tank F not filled
= 1 -
23 =
13 Height of Tank F not filled
=
13 x 57 cm
= 19 cm
Height of Tank E
= 57 - 19 - 5
= 33 cm
Volume of remaining water in Tank E
= 33 x 33 x 23
= 25047 cm
3 Volume of remaining water in Tank F
= 57 x 57 x 23
= 74727 cm
3 Total volume of remaining water in the tank
= 25047 + 74727
= 99774 cm
3
1 ℓ = 1000 cm
3 99774 cm
3 = 99.774 ℓ
Answer(s): (a) 164.436 ℓ; (b) 99.774 ℓ