a box has a square base of side x and height h find the dimensions x, h for which the volume is 14 and the surface area is as small as possible

The dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41

The formula for calculating the volume of the square box is expressed as:

Given that the volume of the box is 14, on substituting the value we will have:

The surface area of the box is expressed as:

To get the surface area is as small as possible, then dS/dx = 0

Get the height of the box. Recall that;

Hence the dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41

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Volume of cuboid :

Surface area of this cuboid :

Putting in above equation, we get :

For minimum area, :

Therefore, value of x is 2.14 .

Hence, this is the required solution.

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: