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

Haiden Davis

Mathematics

12 June, 07:19

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.

+1

Answers (1)

Know the Answer?

Benny · 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