Question

A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 7 cubic meters. Express the total surface area A of the box in terms of the height h (in meters) of the box.

Answer 1

Answer:

Step-by-step explanation:

Given

Box has top and bottom as  square

$Volume =7 m^3$

let l ,b ,h be length, breadth and height of box

l=b because top and bottom as square

thus $volume =b^2\cdot h$

$b^2=\frac{7}{h}$

Total surface area$(TSA)=2\left ( lb+bh+hl\right )$

$TSA=2\left ( b^2+bh+bh\right )$

$TSA=2\left ( b^2+2bh\right )$

$TSA=2\left ( \frac{7}{h}+2h\times \sqrt{\frac{7}{h}}\right )$

$TSA=2\left ( \frac{7}{h}+2\sqrt{7h}\right )$