What is the radius in inches of the base of a cone that will

What is the radius (in inches) of the base of a cone that will have the smallest possible surface area for a volume of 16.5 oz.?

V_cone = 1/3?r²h
SA_cone = ?r(r²+h²)^1/2 + ?r^{2
1 oz = 1.80468751 in3}

Check your formulas with these values:
for r=2 in and h=4 in, V=16.755 in³ and SA=40.666 in²

Solution

V_cone = 1/3pi*r²h

V_cone = 1/3 *pi* 2*2 *4

V_cone =16.755 in^3

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SA_cone = pi*r(r²+h²)^1/2 + pi*r²

SA_cone = pi*2(4+16)^(1/2) +pi*2*2

SA_cone = 40.665 in^2

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