Question

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?

Answer 1

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

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