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# F.2 MATH. AREA

claudia is designing a cylindrical can that will hold 525mL of soup. She uses the design that minimize the surface area. What is the radius of the can?

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- ☂雨後晴空☀Lv 78 years agoFavorite Answer
I use algebra method instead of differentiation since this is a F.2 Maths question.

Assuming the can have a cover.

Note that 1cm³ = 1mL.

Let r (cm) be the radius and h (cm) be the height of the can , then

the volume

= πr² h = 525

the total surface area

= 2πr² + 2πrh

= 2πr² + πrh + πrh

≥ 3 ∛( 2πr² * πrh * πrh).. A.M.≥ G.M. : (a + b + c)/3 ≥ ∛(a b c) for a ,b ,c ≥ 0.

= 3 ∛( 2π (πr² h)² )

= 3 ∛( 2π (525)² ) ,

"=" holds if and only if 2πr² = πrh = πrh , i.e. 2r = h , substitute into πr² h = 525 :πr² 2r = 525

r³ = 525 / (2π)

r = ∛[525 / (2π)] = 4.37...

The radius of the can = 4.37... cm

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