The figure, not drawn to scale, is made of two connected cubical tanks, K and L. Tank K is sealed at the top and completely filled to the brim. Tank L is
23 filled with 106864 mℓ of water. The height of the water level in Tank L is 2 cm higher than that in Tank K. Height of Tank L is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Tank L in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank L = 106864 mℓ
13 of Tank L = 106864 ÷ 2 = 53432 mℓ
33 of Tank L = 53432 x 3 = 160296 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank L = 160296 mℓ = 160.296 ℓ
(b)
Fraction of Tank L not filled
= 1 -
23 =
13 Height of Tank L not filled
=
13 x 69 cm
= 23 cm
Height of Tank K
= 69 - 23 - 2
= 44 cm
Volume of remaining water in Tank K
= 44 x 44 x 31
= 60016 cm
3 Volume of remaining water in Tank L
= 69 x 69 x 31
= 147591 cm
3 Total volume of remaining water in the tank
= 60016 + 147591
= 207607 cm
3
1 ℓ = 1000 cm
3 207607 cm
3 = 207.607 ℓ
Answer(s): (a) 160.296 ℓ; (b) 207.607 ℓ