A box of fixed volume V has a square base with length x. Write a formula for the height, h, of the box in terms of x and V. Sketch a graph of h versus x.
Is the answer h=V/x^2
Yes
To determine the formula for the height of the box, we first need to establish the relationship between the volume V and the given dimensions of the box.
The volume of a box is given by V = L * W * H, where L is the length, W is the width, and H is the height. In this case, we are told that the box has a square base, so the length and width are both x. Therefore, the equation for the volume becomes V = x * x * H, which simplifies to V = x^2 * H.
To find the formula for the height, we can isolate H by dividing both sides of the equation by x^2:
V / x^2 = H
Therefore, the formula for the height of the box (h) in terms of x and V is h = V / x^2.
To sketch a graph of h versus x, we can assume a specific value for V (e.g., 10) and plot points on the graph using different values of x. For each value of x, we can calculate the corresponding height using the formula h = V / x^2. By connecting the plotted points on the graph, we can visualize the relationship between h and x.