Question

e. the distance from the tip of a slice of pizza to the crust is 7 in.
f. breaking a cookie in half creates a straight side 10 cm long.
g. the length of the metal rim around a glass lens is 190 mm.
h. from the center to the edge of a dvd measures 60 mm.
problem 3
a half circle is joined to an equilateral triangle with side lengths of 12 units. what is the perimeter of the resulting shape?
problem 4
circle a has a diameter of 1 foot. circle b has a circumference of 1 meter. which circle is bigger? explain your reasoning. (1 inch = 2.54 centimeters)

Explanation:

Step1: Analyze the perimeter components

The resulting shape's perimeter consists of two sides of the equilateral - triangle and the arc - length of the semi - circle. The side length of the equilateral triangle is \(a = 12\) units. The diameter of the semi - circle is equal to the side length of the equilateral triangle, so \(d=12\) units.

Step2: Calculate the arc - length of the semi - circle

The formula for the circumference of a full circle is \(C=\pi d\). For a semi - circle, the arc - length \(l=\frac{1}{2}\pi d\). Substituting \(d = 12\) into the formula, we get \(l=\frac{1}{2}\pi\times12 = 6\pi\) units.

Step3: Calculate the sum of the two triangle sides

The two sides of the equilateral triangle contribute a length of \(2a\). Since \(a = 12\), the length of the two sides is \(2\times12=24\) units.

Step4: Calculate the perimeter of the resulting shape

The perimeter \(P\) of the resulting shape is the sum of the arc - length of the semi - circle and the lengths of the two sides of the triangle. So \(P=24 + 6\pi\approx24+6\times3.14=24 + 18.84=42.84\) units.

for Problem 4:

Step1: Convert the diameter of circle A to centimeters

The diameter of circle A is \(d_A=1\) foot. Since \(1\) foot \( = 12\) inches and \(1\) inch \(=2.54\) centimeters, then \(d_A=12\times2.54 = 30.48\) centimeters. The circumference of circle A is \(C_A=\pi d_A=\pi\times30.48\approx3.14\times30.48 = 95.45\) centimeters.

Step2: Convert the circumference of circle B to centimeters

The circumference of circle B is \(C_B = 1\) meter. Since \(1\) meter \(=100\) centimeters.

Step3: Compare the circumferences

Since \(C_A\approx95.45\) centimeters and \(C_B = 100\) centimeters, circle B is bigger.

Answer:

\(24 + 6\pi\approx42.84\) units