Question

1 determine the length of the rope. xavier arranges a rope into three semi - circles to form the pattern shown. 8 in. 3 in. 8 in.

Explanation:

Step1: Recall the formula for the circumference of a semi - circle

The formula for the circumference of a semi - circle is $C=\pi r$, where $r$ is the radius.

Step2: Calculate the length of the first semi - circle

The radius of the first semi - circle is $r_1 = 8$ inches. Its length $C_1=\pi r_1=8\pi$ inches.

Step3: Calculate the length of the second semi - circle

The radius of the second semi - circle is $r_2 = 3$ inches. Its length $C_2=\pi r_2 = 3\pi$ inches.

Step4: Calculate the length of the third semi - circle

The radius of the third semi - circle is $r_3 = 8$ inches. Its length $C_3=\pi r_3=8\pi$ inches.

Step5: Find the total length of the rope

The total length $L$ of the rope is the sum of the lengths of the three semi - circles. $L = C_1 + C_2+C_3=(8\pi+3\pi + 8\pi)$ inches. Combining like terms, $L=(8 + 3+8)\pi=19\pi\approx19\times3.14 = 59.66$ inches.

Answer:

$19\pi\approx59.66$ inches