Question

type the correct answer in the box. use numerals instead of words. a cone paper hat is being made for a birthday party, with no gaps or overlaps of material. the radius of the base of the hat is 8 inches and its height is 15 inches. about how many square inches of material is used for the hat? the amount of material used, rounded to the nearest whole number, is about in²

Explanation:

Step1: Calculate the slant height $l$

Use the Pythagorean theorem $l=\sqrt{r^{2}+h^{2}}$, where $r = 8$ inches and $h=15$ inches. So $l=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17$ inches.

Step2: Calculate the lateral - surface area of the cone

The formula for the lateral - surface area of a cone is $A=\pi rl$. Substitute $r = 8$ inches and $l = 17$ inches. Then $A=\pi\times8\times17=136\pi\approx136\times3.14 = 427.04$ square inches.

Step3: Round to the nearest whole number

Rounding $427.04$ to the nearest whole number gives $427$ square inches.

Answer:

427