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 126592 mℓ of water. The height of the water level in Tank F is 4 cm higher than that in Tank E. Height of Tank F is 63 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 = 126592 mℓ
13 of Tank F = 126592 ÷ 2 = 63296 mℓ
33 of Tank F = 63296 x 3 = 189888 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank F = 189888 mℓ = 189.888 ℓ
(b)
Fraction of Tank F not filled
= 1 -
23 =
13 Height of Tank F not filled
=
13 x 63 cm
= 21 cm
Height of Tank E
= 63 - 21 - 4
= 38 cm
Volume of remaining water in Tank E
= 38 x 38 x 23
= 33212 cm
3 Volume of remaining water in Tank F
= 63 x 63 x 23
= 91287 cm
3 Total volume of remaining water in the tank
= 33212 + 91287
= 124499 cm
3
1 ℓ = 1000 cm
3 124499 cm
3 = 124.499 ℓ
Answer(s): (a) 189.888 ℓ; (b) 124.499 ℓ