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Answer:
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
The height of the tin can must be 4 inches
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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Explanation: