The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 46 cm by 26 cm by 26 cm and 2 similar cubes of sides 9 cm. Line W is 12 cm. 14.919 ℓ of water is poured into the top cube into the cuboid.

1. What is the height of the water level from the base of the container?
2. How much more water in cm³ must be poured in so that the water fills up ¹₂ of the top cube?

(a)
Height of the cuboid to the base of side cube
= 26 - 12 - 9
= 5 cm

Volume of water to the base of side cube
= 46 x 26 x 5
= 5980 cm³

Combined base area
= (46 x 26) + (9 x 9)
= 1196 + 81
= 1277 cm²

1 ℓ = 1000 cm3
14.919 ℓ = 14919 cm³

Volume of water in the cube and cuboid beside the cube
= 14919 - 5980
= 8939 cm³

Height of the water in the cube
= 8939 ÷ 1277
= 7 cm

Height of the water level from the base of the container
= 7 + 5
= 12 cm

(b)
Total cubes to be filled
= 1 + ¹₂
= 1¹₂

Total volume to fill up to ¹₂ of the top cube
= (46 x 26 x 26) + (9 x 9 x 9 x 1¹₂)
= 31096 + 1093.5
= 32189.5 cm³ 

1 ℓ = 1000 cm³
14.919 ℓ = 14919 cm³

Extra water to pour in to fill upto half of the top cube
= 32189.5 - 14919
= 17270.5 cm³

Answer(s): (a) 12 cm; (b) 17270.5 cm³