A 9 cm tall cone shaped paper cup can hold up to 58.9 cm3 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.

Volume of cone is given by:

V=1/3πr²h

thus the radius of the cone will be:

58.9=1/3*3.14*r²*9

r²=6.25265

r~2.5 cm

thus the area of the cone will be:

A=πr (r+√ (h²+r²))

A=3.14*2.5 (2.5+√ (2.5²+9²))

A=92.9500 cm²

Thus the area of material needed to make the cup is 92.95 cm²