The figure, not drawn to scale, is made of two connected cubical tanks, C and D. Tank C is sealed at the top and completely filled to the brim. Tank D is
23 filled with 103176 mℓ of water. The height of the water level in Tank D is 2 cm higher than that in Tank C. Height of Tank D is 54 cm. Water is then drained from the container and the height of the water level from the base falls to 26 cm.
- What is the capacity of Tank D in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank D = 103176 mℓ
13 of Tank D = 103176 ÷ 2 = 51588 mℓ
33 of Tank D = 51588 x 3 = 154764 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank D = 154764 mℓ = 154.764 ℓ
(b)
Fraction of Tank D not filled
= 1 -
23 =
13 Height of Tank D not filled
=
13 x 54 cm
= 18 cm
Height of Tank C
= 54 - 18 - 2
= 34 cm
Volume of remaining water in Tank C
= 34 x 34 x 26
= 30056 cm
3 Volume of remaining water in Tank D
= 54 x 54 x 26
= 75816 cm
3 Total volume of remaining water in the tank
= 30056 + 75816
= 105872 cm
3
1 ℓ = 1000 cm
3 105872 cm
3 = 105.872 ℓ
Answer(s): (a) 154.764 ℓ; (b) 105.872 ℓ