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 174090 mℓ of water. The height of the water level in Tank D is 5 cm higher than that in Tank C. Height of Tank D is 65 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 D in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank D = 174090 mℓ
13 of Tank D = 174090 ÷ 2 = 87045 mℓ
33 of Tank D = 87045 x 3 = 261135 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank D = 261135 mℓ = 261.135 ℓ
(b)
Fraction of Tank D not filled
= 1 -
23 =
13 Height of Tank D not filled
=
13 x 65 cm
= 21.666666666667 cm
Height of Tank C
= 65 - 21.666666666667 - 5
= 38.333333333333 cm
Volume of remaining water in Tank C
= 38.333333333333 x 38.333333333333 x 27
= 39674.999999999 cm
3 Volume of remaining water in Tank D
= 65 x 65 x 27
= 114075 cm
3 Total volume of remaining water in the tank
= 39674.999999999 + 114075
= 153750 cm
3
1 ℓ = 1000 cm
3 153750 cm
3 = 153.75 ℓ
Answer(s): (a) 261.135 ℓ; (b) 153.75 ℓ