Question

the formula A=6V^((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 4374in^(2)

Answer 1

The volume of a cube with a surface area of 4374 in^2 is 27 cubic inches.

Step-by-step explanation:

The formula A=6V2/3 relates the surface area, A, in square units, of a cube to the volume, V, in cubic units. To find the volume of a cube with surface area 4374 in2, we can rearrange the formula to solve for volume. We have:

A = 6V2/3

4374 = 6V2/3

Divide both sides by 6:

729 = V2/3

Raise both sides to the power of 3/2:

(729)3/2 = (V2/3)3/2

729 = V2

Take the square root of both sides:

V = √729

V = 27

The volume of the cube is 27 cubic inches.