The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. if a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?

The required height of the tin can is given by the height at the minimum value of the surface area function of the tin can

Reason:

The given information on the tin can are;

Volume of the tin can = 16·π in.³

The amount of tin to be used = Minimum amount

The height of the can in inches required

Solution;

Let h, represent the height of the can, we have;

The surface area of the can, S.A. = 2·π·r² + 2·π·r·h

The volume of the can, V = π·r²·h

Where;

r = The radius of the tin can

h = The height of the tin can

Which gives;

16·π = π·r²·h

16 = r²·h

Which gives;

When the minimum amount of tin is used, we have;

Therefore;

4·π·(r³ - 8) = r² × 0

r³ = 8

r = 2

The radius of the tin can, r = 2 inches

The

The height of the tin can, h = 4 inches

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The required height of can is 4 inches.

Given data:

The volume of cylindrical tin with top and bottom is, .

The volume of tin is,

here, r is the radius of can and h is the height of can.

The surface area of tin is,

For minimum amount of tin used, we have,

So, height of can is,

Thus, the required height of can is 4 inches.

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