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
34 filled with 120129 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 68 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Tank L in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank L = 120129 mℓ
14 of Tank L = 120129 ÷ 3 = 40043 mℓ
44 of Tank L = 40043 x 4 = 160172 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank L = 160172 mℓ = 160.172 ℓ
(b)
Fraction of Tank L not filled
= 1 -
34 =
14 Height of Tank L not filled
=
14 x 68 cm
= 17 cm
Height of Tank K
= 68 - 17 - 2
= 49 cm
Volume of remaining water in Tank K
= 49 x 49 x 25
= 60025 cm
3 Volume of remaining water in Tank L
= 68 x 68 x 25
= 115600 cm
3 Total volume of remaining water in the tank
= 60025 + 115600
= 175625 cm
3
1 ℓ = 1000 cm
3 175625 cm
3 = 175.625 ℓ
Answer(s): (a) 160.172 ℓ; (b) 175.625 ℓ