Final answer:
To find the height of the box, set the equation for volume equal to the known value and solve for d. Then substitute the value of d into the equation for height.
Step-by-step explanation:
To determine the height of the box, we need to find the value of d in the equation for the volume. The volume of the box is given as (d³ + 100) cm³. We can set this expression equal to the known value of the volume and solve for d. Once we have the value of d, we can substitute it into the expression for the height of the box, which is given by the equation (d² – 10d + 100).
First, let's set the equation for the volume equal to the known value and solve for d:
(d³ + 100) = (given volume)
Next, let's substitute the value of d into the equation for the height:
(d² – 10d + 100) = height of the box
Solve these equations for d and the height of the box, respectively.