For a closed cylinder with radius r ⁢ cm and height h ⁢ cm, find the dimensions giving the minimum surface area, given that the volume is 36 cm3.

The radius is 1.79 cm and height is 3.58 cm.

Step-by-step explanation:

The surface area of the closed cylinder is given by,

And volume is given by,

Where, R is radius and h is height of cylinder.

Volume is given to be  36 cm3.

Inserting this value of h in Surface area equation, we get,

Now differentiating wrt x to find minimum, inserting , we get,

Thus, h = 3.58 cm from above equation.

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the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!