Mathematics: Three cube-shaped aquariums that are five inches on each side are filled with water to capacity. all of the water from those three aquariums is to be transferred into a larger cube aquarium so that it must be filled to at least 50% of its total capacity without overflowing. which of the following could be the length, in inches, of a side of the larger aquarium? (a) 6.9 (b) 8.4 (c) 9.5

b. y = 2/3x + 2Step-by-step explanation:...

Three cube-shaped aquariums that are five inches

amoakoh800003

30.12.2021

(B) 8.4

Step-by-step explanation:

Given : Dimension of each cube = 5 inches

Then, volume of each cube = $(5)^3=125\text{ in.}^3$

Then, volume of 3 such cubes = $3\times125=375\text{ in.}^3$

Let x be the dimension of larger cube , then its volume = x^3

Now, by considering the given question, we have

$0.50 x^3\leq375\\\\\Rightarrow\ x^2\leq\dfrac{375}{0.5}\\\\\Rightarrow\ x^3\leq750$

Taking cube-root on both sides , we get

$x\leq(750)^{1/3}\\\\\Rightarrow\ x\leq9.086$

The most nearest value from the options less than 9.086 is 8.4.

Hence, the the length of a side of the larger aquarium could be 8.4 inches.

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