The length of each edge of a cube is decreased by 40 percent By what percent does the volume of the cube decrease? Express your answer to the nearest tenth.

78% (to the nearest tenth)

Step-by-step explanation:

Volume of a cube = (length) ³

Let the length of the cube = y

Original volume = y³

if the length is decreased by 40%, then new length = 1 - (40% of y)

= 1-0.4y

= 0.6%

New volume (after decreasing the length) = (0.6y) ³

= 0.216‬‬y³

% Volume decrease = (Original volume - New volume) / Original Volume x 100%

= (y³ - 0.216‬‬y³) / y³ x 100%

= 0.784y³/y³ x 100%

=78.4%

≈78%

78.4%

Step-by-step explanation:

After the decrease, the edge length is 0.6 of what it was. Then the volume is 0.6^3 = 0.216 of what it was. That's a decrease of ...

1 - 0.216 = 0.784 = 78.4%

The volume of the cube has decreased 78.4%.