Question

1. miriam is sewing an appliqué of an ice cream cone on a flag which the local ice cream shop will use as a display for advertisement. use the diagram to find the amount of material needed for the ice cream cone appliqué.

Explanation:

Step1: Calculate area of semi - circle

The diameter of the semi - circle is $d = 8$ in, so the radius $r=\frac{d}{2}=\frac{8}{2}=4$ in. The area of a full - circle is $A_{circle}=\pi r^{2}$, and the area of a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi(4)^{2}=8\pi$ square inches.

Step2: Calculate lateral area of cone

The formula for the lateral area of a cone is $A_{lateral}=\pi rl$, where $r$ is the radius of the base of the cone and $l$ is the slant height. First, we find the slant height $l$ using the Pythagorean theorem. The height of the cone $h = 15$ in and $r = 4$ in. So, $l=\sqrt{h^{2}+r^{2}}=\sqrt{15^{2}+4^{2}}=\sqrt{225 + 16}=\sqrt{241}\approx15.52$ in. Then the lateral area of the cone $A_{lateral}=\pi\times4\times15.52 = 62.08\pi$ square inches.

Step3: Calculate total area

The total area of the ice - cream cone appliqué $A = A_{semicircle}+A_{lateral}=8\pi+62.08\pi=70.08\pi\approx70.08\times3.14 = 220$ square inches.

Answer:

Approximately 220 square inches.