Emma filled a rectangular container which had a base area of 40 cm
2 and a height of 30.9 cm with water. Then, she placed 12 identical metal cubes into this container. As a result, the height of the water in the rectangular container increased by 37.5 cm.
- What was the length of each side of the metal cube?
- After Emma removed the metal cubes from the container, she poured all the water from the container to fill bottles of 0.39 ℓ. What was the maximum number of bottles she could fill?
(a)
Volume of 12 cubes
= 40 x 37.5
= 1500 cm
3
Volume of 1 cube
= 1500 ÷ 12
= 125 cm
3
Length of the cube
= ³√125
= 5 cm
(b)
Volume of water
= 40 x 30.9
= 1236 cm
3 Number of bottles that Emma can fill
= 1236 ÷ 390
= 3 r 66
Maximum number of bottles that Emma can fill = 3
Answer(s): (a) 5 cm; (b) 3