The figure, not drawn to scale, is made of two connected cubical tanks, G and H. Tank G is sealed at the top and completely filled to the brim. Tank H is
23 filled with 182490 mℓ of water. The height of the water level in Tank H is 5 cm higher than that in Tank G. Height of Tank H is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Tank H in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank H = 182490 mℓ
13 of Tank H = 182490 ÷ 2 = 91245 mℓ
33 of Tank H = 91245 x 3 = 273735 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank H = 273735 mℓ = 273.735 ℓ
(b)
Fraction of Tank H not filled
= 1 -
23 =
13 Height of Tank H not filled
=
13 x 70 cm
= 23.333333333333 cm
Height of Tank G
= 70 - 23.333333333333 - 5
= 41.666666666667 cm
Volume of remaining water in Tank G
= 41.666666666667 x 41.666666666667 x 27
= 46875.000000001 cm
3 Volume of remaining water in Tank H
= 70 x 70 x 27
= 132300 cm
3 Total volume of remaining water in the tank
= 46875.000000001 + 132300
= 179175 cm
3
1 ℓ = 1000 cm
3 179175 cm
3 = 179.175 ℓ
Answer(s): (a) 273.735 ℓ; (b) 179.175 ℓ