Question

9. Write the formula for the volume of a rectangular box, V = lwh, in terms of h. Then find the height of abox for which V = 96 cm, 1 = 8 cm, and w = 2 cm.??

Answer 1

To find the formula of the box in terms of h, we just need to isolate the term h.

We can do that by dividing both sides of the volume equation by 'lw':

`\begin{gathered} V=l\cdot w\cdot h \\ (V)/(l\cdot w)=(l\cdot w\cdot h)/(l\cdot w) \\ (V)/(l\cdot w)=h \end{gathered}`

Then, to find the height of the box for which V = 96, l = 8 and w = 2, we just need to apply these values in the equation to calculate the value of h:

`\begin{gathered} (V)/(l\cdot w)=h \\ (96)/(8\cdot2)=h \\ (96)/(16)=h \\ h=6\text{ cm} \end{gathered}`

So we have that the height of the box is 6 centimeters.