Respuesta :
Answer:
Step-by-step explanation:
Given
Box has top and bottom as square
[tex]Volume =7 m^3 [/tex]
let l ,b ,h be length, breadth and height of box
l=b because top and bottom as square
thus [tex]volume =b^2\cdot h[/tex]
[tex]b^2=\frac{7}{h}[/tex]
Total surface area[tex](TSA)=2\left ( lb+bh+hl\right )[/tex]
[tex]TSA=2\left ( b^2+bh+bh\right )[/tex]
[tex]TSA=2\left ( b^2+2bh\right )[/tex]
[tex]TSA=2\left ( \frac{7}{h}+2h\times \sqrt{\frac{7}{h}}\right )[/tex]
[tex]TSA=2\left ( \frac{7}{h}+2\sqrt{7h}\right )[/tex]
You can use the volume of cuboid to find the needed expression.
The surface area A of the box in terms of the height h (in meters) of the box is given as
[tex]A = \dfrac{14 + h\sqrt{h} \times 4\sqrt{7}}{h}[/tex] square feet.
How to find the volume of cuboid?
Let the three dimensions(height, length, width) be x, y,z units respectively.
Then the volume of the cuboid is given as
[tex]V = x \times y \times z \: \rm unit^3[/tex]
What is the surface area of cuboid?
Let the three dimensions(height, length, width) be x, y,z units respectively.
The surface area of the cuboid is given by
[tex]S = 2(a\times b + b\times c + c\times a)[/tex]
Using the above facts, calculating the surface area of the box
Let the squares on top and bottom be of edge 'd meters'
The height is given to be h meters.
Thus, volume is given as
[tex]h \times s \times s = 7\\hs^2 = 7\\\\s = \sqrt{\dfrac{7}{h}} \text{\: (Positive root since s is length's measure, thus non negative quantity)}[/tex]
Finding the surface area:
[tex]A= 2(h \times \sqrt{7/h} + \sqrt{7/h} \times \sqrt{7/h} + \sqrt{7/h} \times h) = \dfrac{14 + h\sqrt{h} \times 4\sqrt{7}}{h}[/tex]
The surface area A of the box in terms of the height h (in meters) of the box is given as
[tex]A = \dfrac{14 + h\sqrt{h} \times 4\sqrt{7}}{h}[/tex] square feet.
Learn more about volume of cuboid here:
https://brainly.com/question/46030
