A box with a square base and no top has a volume of 6 cubic meters. Express the total surface area, A, of the box as a function of the width, W, of the base?

Question

anonymous · Answer

x=57.3 plusorminus 2 pi n

anonymous · Answer

sorry. i responded to the wrong person

campbell_st · Answer

so the square base has dimensions w and height h

Area = w^2

then volume 

64 = w^2h

so 

$$h = \frac{64}{w^2}$$

so in terms of surface area, the square base has and area 

$$A= w^2$$

and the 4 rectangular sides 

$$A = t \times w \times h$$

so the surface area is 

$$SA = w^2 + 4wh$$

now subsitute h and you get 

$$SA = w^2 + \frac{64w}{w^2}$$

or 

$$SA = w^2 + \frac{64}{w}$$

campbell_st · Answer

oops 4 rectangular sides have 

$$A = 4 \times w \times h$$

campbell_st · Answer

hope it helps

anonymous · Answer

surface area without top means,
$$SA = SA(base) + 4*SA(sides)$$
assume width=x and height=y
so volume of box= $$x^2y$$
$$6/x^2=y$$
Now substitute y value in above equation ....

anonymous · Answer

surface area of base is $$x^2$$ and surface area of 4 sides =4*x*y

anonymous · Answer

Refer to the Mathematica solution attached.