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The formula A=6V exponent 2/3 relates the surface area A, in square units, of a cube to the volume V, in cubic units. What is the volume, in cubic inches, of a cube with surface area 486 in.2?

Respuesta :

sqdancefan

Answer:

729 in³

Step-by-step explanation:

Fill in the given numbers in the formula and solve for V.

... A = 6V^(2/3) . . . . . . the given formula

... 486 = 6V^(2/3) . . . . with the given area filled in

... 81 = V^(2/3) . . . . . . . divide by 6

... 81^(3/2) = V . . . . . . . raise to the 3/2 power. (2/3)·(3/2) = 1, so we have V on the right

... 729 = V . . . . in³

_____

You may have noticed that (81 in²)^(3/2) becomes 729 in³. The exponent operations work on the units, too.

MrRoyal

The area of a shape is the amount of space the shape occupies, while the volume is the amount of space in it.

The equation is given as:

[tex]A = 6V^\frac 23[/tex]

First, we make V the subject of formula

Divide both sides by 6

[tex]\frac A6 = V^\frac 23[/tex]

Take 3/2th root of both sides

[tex](\frac A6)^\frac 32 = V[/tex]

Rewrite as:

[tex]V = (\frac A6)^\frac 32[/tex]

Substitute 486 for A

[tex]V = (\frac{486}6)^\frac 32[/tex]

[tex]V = (81)^\frac 32[/tex]

Express 81 as [tex]9^2[/tex]

[tex]V = (9^2)^\frac 32[/tex]

[tex]V = 9^3[/tex]

[tex]V = 729[/tex]

Hence, the volume is 729[tex]in^3[/tex]

Read more about areas and volumes at:

https://brainly.com/question/3628550

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