Esther filled a rectangular tank which had a base area of 96 cm
2 and a height of 36.1 cm with water. Then, she placed 12 identical metal cubes into this tank. As a result, the height of the water in the rectangular tank increased by 64 cm.
- What was the length of each side of the metal cube?
- After Esther removed the metal cubes from the tank, she poured all the water from the tank to fill bottles of 0.16 ℓ. What was the maximum number of bottles she could fill?
(a)
Volume of 12 cubes
= 96 x 64
= 6144 cm
3
Volume of 1 cube
= 6144 ÷ 12
= 512 cm
3
Length of the cube
= ³√512
= 8 cm
(b)
Volume of water
= 96 x 36.1
= 3465.6 cm
3 Number of bottles that Esther can fill
= 3465.6 ÷ 160
= 21 r 105.6
Maximum number of bottles that Esther can fill = 21
Answer(s): (a) 8 cm; (b) 21