A rectangular prism has a length of 4x inches, a width of 3x inches, and a height of 5x inches. If the prism has a volume of 20,580 cubic inches, find the value of x.
To find the value of x, we can use the formula for the volume of a rectangular prism:
Volume = Length * Width * Height
Given that the length is 4x inches, the width is 3x inches, and the height is 5x inches, we can substitute these values into the formula:
20,580 = (4x) * (3x) * (5x)
Now, let's simplify this equation:
20,580 = 60x^3
To solve for x, we need to isolate it on one side of the equation. Divide both sides of the equation by 60:
(20,580 / 60) = (60x^3 / 60)
343 = x^3
To find the value of x, we need to find the cube root of both sides of the equation:
∛343 = ∛x^3
7 = x
Therefore, the value of x is 7.
(3x)(4x)(5x) = 20580
60x^3 = 20580
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