A 9 cm tall cone shaped paper cup can hold up to 58.9 cm cubed of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.

Question

Mathematics

Amira Ford

25 May, 18:08

A 9 cm tall cone shaped paper cup can hold up to 58.9 cm cubed of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.

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Salvador Hartman · Answer 1

Volume of a cone, V = πr^2h/3

r = Sqrt 3V/πh = Sqrt [ (58.9*3) / (3.14*9) ] = 2.5 cm, minimum

Surface area, A = πr [r + Sqrt (h^2+r^2) ] = 3.14*2.5*[2.5 + Sqrt (9^2+2.5^2) ] = 92.95 cm^2

Therefore, minimum amount of paper required is 92.95 cm^2