Cone party hat situation

Question

Alex made a paper party hat, (cone) with a slant height of 6 inches and a height of 5 inches. How many square feet of poke dot paper would be needed to create 20 of these hats for your friends?

Answer 1

We are going to use the formula for the lateral surface area of a cone. The formula is S.A.=π*L√(L² - h²) where L is the slant height and h is the height. The problem is asking us for the answer in square feet but we are given the information in inches. It is easier to convert them at the beginning of the problem so we don't forget to at the end. h= 5 inches becomes h=0.417 feet when we divide by 12 and and L=6 inches becomes L=0.5 feet.

S.A. =π(0.5)√[(0.5)²-(0.417)²]=0.5π√(0.25 - 0.174)= 0.5π√0.076 ≈ 0.5π(0.276) ≈ 0.433 square feet for each hat. To find the total for 20 hats we multiply this number by 20 which gives us...

8.66 square feet.

I hope this is helpful!