emma3001 said:Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.
The formula for finding the volume of a cube is V = s^3, where s is the length of one side of the cube. This means that you would multiply the side length by itself three times to find the volume.
The side length of a cube directly affects its volume. As the side length increases, the volume also increases. This is because the volume is proportional to the cube of the side length (V = s^3), meaning that even a small increase in side length can result in a significant increase in volume.
The units for measuring volume can vary depending on the system of measurement being used. In the metric system, the standard unit for volume is cubic meters (m^3). In the imperial system, the standard unit for volume is cubic feet (ft^3). Other common units for volume include liters, gallons, and cubic centimeters.
No, the volume of a cube cannot be negative. Volume is a measure of how much space an object occupies, and since a cube cannot have a negative amount of space, its volume cannot be negative.
The volume of a cube and its surface area are related, but they are not the same thing. The surface area of a cube is the total area of all its surfaces, while the volume is the amount of space inside the cube. The surface area increases at a faster rate than the volume as the side length increases. Specifically, the surface area increases at a rate of s^2, while the volume increases at a rate of s^3.