Find the least amount of paper that can form the cone-shaped cup. (Round your answer to two decimal places.)

Question

The circumference of the top rim of the cone-shaped paper cup is 7.87 inches with a slant height of 3.8 inches Find the least amount of paper that can form the cone-shaped cup. (Round your answer to two decimal places.)

Answer 1

The equation of the circumference of the rim of the cone is:

C = 2πr

We can calculate the radius to be:

r = C / 2π

The equation for the surface area of the cone is:

SA = πrl

So if we make our substitution for r:

SA = π * (C / 2π) * l

And now when we plug in the given values for C and l, we get:

SA = π * (7.87 / 2π) * 3.8

= 14.95 in²