The figure is not drawn to scale. It shows an empty container made up of a cuboid, measuring 40 cm by 24 cm by 24 cm and 2 similar cubes of sides 8 cm. Line R is 11 cm. 9.92 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 15 of the top cube?
(a)
Height of the cuboid to the base of side cube
= 24 - 11 - 8
= 5 cm
Volume of water to the base of side cube
= 40 x 24 x 5
= 4800 cm
3Combined base area
= (40 x 24) + (8 x 8)
= 960 + 64
= 1024 cm
21 ℓ = 1000 cm3
9.92 ℓ = 9920 cm
3Volume of water in the cube and cuboid beside the cube
= 9920 - 4800
= 5120 cm
3Height of the water in the cube
= 5120 ÷ 1024
= 5 cm
Height of the water level from the base of the container
= 5 + 5
= 10 cm
(b)
Total cubes to be filled
= 1 +
15= 1
15 Total volume to fill up to
15 of the top cube
= (40 x 24 x 24) + (8 x 8 x 8 x 115)
= 23040 + 614.4 = 23654.4 cm
3 1 ℓ = 1000 cm
3
9.92 ℓ = 9920 cm
3 Extra water to pour in to fill upto half of the top cube
= 23654.4 - 9920
= 13734.4 cm
3 Answer(s): (a) 10 cm; (b) 13734.4 cm
3