The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 42 cm by 28 cm by 28 cm and 2 similar cubes of sides 6 cm. Line G is 8 cm. 20.1 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
= 28 - 8 - 6
= 14 cm
Volume of water to the base of side cube
= 42 x 28 x 14
= 16464 cm
3Combined base area
= (42 x 28) + (6 x 6)
= 1176 + 36
= 1212 cm
21 ℓ = 1000 cm3
20.1 ℓ = 20100 cm
3Volume of water in the cube and cuboid beside the cube
= 20100 - 16464
= 3636 cm
3Height of the water in the cube
= 3636 ÷ 1212
= 3 cm
Height of the water level from the base of the container
= 3 + 14
= 17 cm
(b)
Total cubes to be filled
= 1 +
14= 1
14 Total volume to fill up to
14 of the top cube
= (42 x 28 x 28) + (6 x 6 x 6 x 114)
= 32928 + 270 = 33198 cm
3 1 ℓ = 1000 cm
3
20.1 ℓ = 20100 cm
3 Extra water to pour in to fill upto half of the top cube
= 33198 - 20100
= 13098 cm
3 Answer(s): (a) 17 cm; (b) 13098 cm
3