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 7 cm. Line M is 12 cm. 15.484 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
= 28 - 12 - 7
= 9 cm
Volume of water to the base of side cube
= 42 x 28 x 9
= 10584 cm
3Combined base area
= (42 x 28) + (7 x 7)
= 1176 + 49
= 1225 cm
21 ℓ = 1000 cm3
15.484 ℓ = 15484 cm
3Volume of water in the cube and cuboid beside the cube
= 15484 - 10584
= 4900 cm
3Height of the water in the cube
= 4900 ÷ 1225
= 4 cm
Height of the water level from the base of the container
= 4 + 9
= 13 cm
(b)
Total cubes to be filled
= 1 +
12= 1
12 Total volume to fill up to
12 of the top cube
= (42 x 28 x 28) + (7 x 7 x 7 x 112)
= 32928 + 514.5 = 33442.5 cm
3 1 ℓ = 1000 cm
3
15.484 ℓ = 15484 cm
3 Extra water to pour in to fill upto half of the top cube
= 33442.5 - 15484
= 17958.5 cm
3 Answer(s): (a) 13 cm; (b) 17958.5 cm
3