Olivia filled a rectangular container which had a base area of 75 cm
2 and a height of 20.9 cm with water. Then, she placed 8 identical metal cubes into this container. As a result, the height of the water in the rectangular container increased by 23.04 cm.
- What was the length of each side of the metal cube?
- After Olivia removed the metal cubes from the container, she poured all the water from the container to fill bottles of 0.53 ℓ. What was the maximum number of bottles she could fill?
(a)
Volume of 8 cubes
= 75 x 23.04
= 1728 cm
3
Volume of 1 cube
= 1728 ÷ 8
= 216 cm
3
Length of the cube
= ³√216
= 6 cm
(b)
Volume of water
= 75 x 20.9
= 1567.5 cm
3 Number of bottles that Olivia can fill
= 1567.5 ÷ 530
= 2 r 507.5
Maximum number of bottles that Olivia can fill = 2
Answer(s): (a) 6 cm; (b) 2