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
23 filled with 129928 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 63 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.
- What is the capacity of Tank S in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank S = 129928 mℓ
13 of Tank S = 129928 ÷ 2 = 64964 mℓ
33 of Tank S = 64964 x 3 = 194892 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank S = 194892 mℓ = 194.892 ℓ
(b)
Fraction of Tank S not filled
= 1 -
23 =
13 Height of Tank S not filled
=
13 x 63 cm
= 21 cm
Height of Tank R
= 63 - 21 - 1
= 41 cm
Volume of remaining water in Tank R
= 41 x 41 x 29
= 48749 cm
3 Volume of remaining water in Tank S
= 63 x 63 x 29
= 115101 cm
3 Total volume of remaining water in the tank
= 48749 + 115101
= 163850 cm
3
1 ℓ = 1000 cm
3 163850 cm
3 = 163.85 ℓ
Answer(s): (a) 194.892 ℓ; (b) 163.85 ℓ