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 105066 mℓ of water. The height of the water level in Tank L is 5 cm higher than that in Tank K. Height of Tank L is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.

1. What is the capacity of Tank L in litres?
2. What is the volume of water in the tank now in litres?

(a)
²₃ of Tank L = 105066 mℓ
¹₃ of Tank L = 105066 ÷ 2 = 52533 mℓ
³₃ of Tank L = 52533 x 3 = 157599 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank L = 157599 mℓ = 157.599 ℓ

(b)
Fraction of Tank L not filled
= 1 - ²₃
= ¹₃

Height of Tank L not filled
= ¹₃ x 66 cm
= 22 cm

Height of Tank K
= 66 - 22 - 5
= 39 cm

Volume of remaining water in Tank K
= 39 x 39 x 34
= 51714 cm³ 

Volume of remaining water in Tank L
= 66 x 66 x 34
= 148104 cm³ 

Total volume of remaining water in the tank
= 51714 + 148104
= 199818 cm³

1 ℓ = 1000 cm³
199818 cm³ = 199.818 ℓ

Answer(s): (a) 157.599 ℓ; (b) 199.818 ℓ