Gem filled a rectangular tank which had a base area of 100 cm
2 and a height of 37.3 cm with water. Then, she placed 8 identical metal cubes into this tank. As a result, the height of the water in the rectangular tank increased by 80 cm.
- What was the length of each side of the metal cube?
- After Gem removed the metal cubes from the tank, she poured all the water from the tank to fill bottles of 0.82 ℓ. What was the maximum number of bottles she could fill?
(a)
Volume of 8 cubes
= 100 x 80
= 8000 cm
3
Volume of 1 cube
= 8000 ÷ 8
= 1000 cm
3
Length of the cube
= ³√1000
= 10 cm
(b)
Volume of water
= 100 x 37.3
= 3730 cm
3 Number of bottles that Gem can fill
= 3730 ÷ 820
= 4 r 450
Maximum number of bottles that Gem can fill = 4
Answer(s): (a) 10 cm; (b) 4