Question

A rectangular box has a volume x^3-64 cubic inches. If the height of the box x-4 inches, what is the area of the base of the box, in square inches ?

Answer 1

Answer:

$\purple{ \bold{ \therefore \: A_{base} = {x}^{2} + 4x + 16}}$

Step-by-step explanation:

$\because \: V_{box} = A_{base} \times height \\ \\ \therefore \: A_{base} = \frac{V_{box}}{height} \\ \\ \therefore \: A_{base} = \frac{ {x}^{3} - 64}{(x - 4)} \\ \\ \therefore \: A_{base} = \frac{ {x}^{3} - {4}^{3} }{(x - 4)} \\ \\ \therefore \: A_{base} = \frac{ \cancel{ ({x} - {4})}( {x}^{2} + 4x + {4}^{2} )}{\cancel{ ({x} - {4})}} \\ \\ \purple{ \bold{ \therefore \: A_{base} = {x}^{2} + 4x + 16}}$