The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 40 cm by 28 cm by 28 cm and 2 similar cubes of sides 8 cm. Line M is 9 cm. 19.424 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 - 9 - 8
= 11 cm
Volume of water to the base of side cube
= 40 x 28 x 11
= 12320 cm
3Combined base area
= (40 x 28) + (8 x 8)
= 1120 + 64
= 1184 cm
21 ℓ = 1000 cm3
19.424 ℓ = 19424 cm
3Volume of water in the cube and cuboid beside the cube
= 19424 - 12320
= 7104 cm
3Height of the water in the cube
= 7104 ÷ 1184
= 6 cm
Height of the water level from the base of the container
= 6 + 11
= 17 cm
(b)
Total cubes to be filled
= 1 +
14= 1
14 Total volume to fill up to
14 of the top cube
= (40 x 28 x 28) + (8 x 8 x 8 x 114)
= 31360 + 640 = 32000 cm
3 1 ℓ = 1000 cm
3
19.424 ℓ = 19424 cm
3 Extra water to pour in to fill upto half of the top cube
= 32000 - 19424
= 12576 cm
3 Answer(s): (a) 17 cm; (b) 12576 cm
3