The volume of the cube can be expressed as a function of m, the number of minutes elapsed as V(m) = (3 + 4m)³ feet³.
What do we mean by volume?
The volume of an object is the total space occupied by the object in the three-dimensional space.
How do we solve the given question?
In the question, we are asked to express the volume of a cube as a function of m, the number of minutes elapsed. We are given that the initial length of the edge of the cube was 3 feet, and it increases at a rate of 4 feet per minute.
∴ We can say that the length of the edge after m minutes = 3 + 4m
As 4 feet is the increase per minute and m minutes have elapsed.
We know, that the volume of a cube is the cube of the length of the edge.
∴ The volume = (3 + 4m)³.
Hence, the function of the volume of the cube in m can be written as,
V(m) = (3 + 4m)³ feet³.
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