The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 44 cm by 22 cm by 22 cm and 2 similar cubes of sides 8 cm. Line R is 10 cm. 10.064 ℓ of water is poured into the top cube into the cuboid.
- What is the height of the water level from the base of the container?
- How much more water in cm3 must be poured in so that the water fills up 14 of the top cube?
(a)
Height of the cuboid to the base of side cube
= 22 - 10 - 8
= 4 cm
Volume of water to the base of side cube
= 44 x 22 x 4
= 3872 cm
3Combined base area
= (44 x 22) + (8 x 8)
= 968 + 64
= 1032 cm
21 ℓ = 1000 cm3
10.064 ℓ = 10064 cm
3Volume of water in the cube and cuboid beside the cube
= 10064 - 3872
= 6192 cm
3Height of the water in the cube
= 6192 ÷ 1032
= 6 cm
Height of the water level from the base of the container
= 6 + 4
= 10 cm
(b)
Total cubes to be filled
= 1 +
14= 1
14 Total volume to fill up to
14 of the top cube
= (44 x 22 x 22) + (8 x 8 x 8 x 114)
= 21296 + 640 = 21936 cm
3 1 ℓ = 1000 cm
3
10.064 ℓ = 10064 cm
3 Extra water to pour in to fill upto half of the top cube
= 21936 - 10064
= 11872 cm
3 Answer(s): (a) 10 cm; (b) 11872 cm
3