The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 42 cm by 22 cm by 22 cm and 2 similar cubes of sides 8 cm. Line K is 12 cm. 6.788 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 12 of the top cube?
(a)
Height of the cuboid to the base of side cube
= 22 - 12 - 8
= 2 cm
Volume of water to the base of side cube
= 42 x 22 x 2
= 1848 cm
3Combined base area
= (42 x 22) + (8 x 8)
= 924 + 64
= 988 cm
21 ℓ = 1000 cm3
6.788 ℓ = 6788 cm
3Volume of water in the cube and cuboid beside the cube
= 6788 - 1848
= 4940 cm
3Height of the water in the cube
= 4940 ÷ 988
= 5 cm
Height of the water level from the base of the container
= 5 + 2
= 7 cm
(b)
Total cubes to be filled
= 1 +
12= 1
12 Total volume to fill up to
12 of the top cube
= (42 x 22 x 22) + (8 x 8 x 8 x 112)
= 20328 + 768 = 21096 cm
3 1 ℓ = 1000 cm
3
6.788 ℓ = 6788 cm
3 Extra water to pour in to fill upto half of the top cube
= 21096 - 6788
= 14308 cm
3 Answer(s): (a) 7 cm; (b) 14308 cm
3