The figure, not drawn to scale, is made of two connected cubical tanks, S and T. Tank S is sealed at the top and completely filled to the brim. Tank T is
34 filled with 141015 mℓ of water. The height of the water level in Tank T is 2 cm higher than that in Tank S. Height of Tank T is 67 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Tank T in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank T = 141015 mℓ
14 of Tank T = 141015 ÷ 3 = 47005 mℓ
44 of Tank T = 47005 x 4 = 188020 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank T = 188020 mℓ = 188.02 ℓ
(b)
Fraction of Tank T not filled
= 1 -
34 =
14 Height of Tank T not filled
=
14 x 67 cm
= 16.75 cm
Height of Tank S
= 67 - 16.75 - 2
= 48.25 cm
Volume of remaining water in Tank S
= 48.25 x 48.25 x 32
= 74498 cm
3 Volume of remaining water in Tank T
= 67 x 67 x 32
= 143648 cm
3 Total volume of remaining water in the tank
= 74498 + 143648
= 218146 cm
3
1 ℓ = 1000 cm
3 218146 cm
3 = 218.146 ℓ
Answer(s): (a) 188.02 ℓ; (b) 218.146 ℓ