The figure, not drawn to scale, is made of two connected cubical tanks, R and S. Tank R is sealed at the top and completely filled to the brim. Tank S is
45 filled with 128508 mℓ of water. The height of the water level in Tank S is 1 cm higher than that in Tank R. Height of Tank S is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Tank S in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank S = 128508 mℓ
15 of Tank S = 128508 ÷ 4 = 32127 mℓ
55 of Tank S = 32127 x 5 = 160635 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank S = 160635 mℓ = 160.635 ℓ
(b)
Fraction of Tank S not filled
= 1 -
45 =
15 Height of Tank S not filled
=
15 x 66 cm
= 13.2 cm
Height of Tank R
= 66 - 13.2 - 1
= 51.8 cm
Volume of remaining water in Tank R
= 51.8 x 51.8 x 25
= 67081 cm
3 Volume of remaining water in Tank S
= 66 x 66 x 25
= 108900 cm
3 Total volume of remaining water in the tank
= 67081 + 108900
= 175981 cm
3
1 ℓ = 1000 cm
3 175981 cm
3 = 175.981 ℓ
Answer(s): (a) 160.635 ℓ; (b) 175.981 ℓ