Question

choose the formula you would use to solve the following related rates problem: all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing each edge is 1 centimeter.

Explanation:

The problem is about the volume of a cube. The formula for the volume \( V \) of a cube with edge length \( s \) is \( V = s^3 \) (note: in the options, it's written as \( V = s^3 \) perhaps with a typo as \( V = s^5 \) is incorrect, but likely the intended is \( V = s^3 \); however, among the given options, the volume formula for a cube (since all edges are equal) should be \( V = s^3 \), but if we consider the options, the one that represents the volume of a cube (as opposed to area of a square \( A = s^2 \), area of a rectangle \( A = l*w \), or incorrect volume) – the correct volume formula for a cube is \( V = s^3 \), but in the options, the one labeled \( V = s^5 \) is likely a typo, but more accurately, the volume of a cube is \( V = s^3 \), so the option with \( V = s^3 \) (even if miswritten as \( V = s^5 \) maybe a display error) – but the key is that the volume of a cube is \( V = s^3 \), so we choose the formula for the volume of a cube.

Answer:

The option with \( V = s^3 \) (assuming the \( s^5 \) is a typo; among the given, the volume formula for a cube is \( V = s^3 \), so the option labeled \( V = s^5 \) might be incorrect, but the correct volume formula for a cube is \( V = s^3 \), so we select the volume formula for the cube, which is \( V = s^3 \) (the option with \( V = s^3 \) - if we take the options, the one with \( V = s^3 \) (or the one intended for cube volume)).