Question

find the circumference and area of each circle. use 3.14 for pi
7
6
find the perimeter and area of each semicircle. use 3.14 for pi.
9
10

1. mario paints a circular sign with a diameter of 10 feet. to the nearest square foot, how much area does the paint cover?
2. the circumference of a circle was 100 inches. what is the approximate length of its diameter? use 3.14 for pi.

Explanation:

Let's solve for the semicircle labeled 9 (diameter 12.5 units, using \( \pi = 3.14 \)).

Step 1: Find the radius

The radius \( r \) is half the diameter. So \( r=\frac{12.5}{2} = 6.25 \) units.

Step 2: Calculate the perimeter of the semicircle

The perimeter of a semicircle (\( P \)) is the sum of the half - circumference and the diameter. The formula for the circumference of a full circle is \( C = 2\pi r \), so the half - circumference is \( \frac{1}{2}(2\pi r)=\pi r \). Then the perimeter of the semicircle is \( P=\pi r + d \) (where \( d \) is the diameter).

Substitute \( r = 6.25 \), \( \pi=3.14 \) and \( d = 12.5 \):

\( P=3.14\times6.25+12.5 \)

\( 3.14\times6.25 = 19.625 \)

\( P=19.625 + 12.5=32.125 \) units.

Step 3: Calculate the area of the semicircle

The area of a full circle is \( A_{full}=\pi r^{2} \), so the area of a semicircle (\( A \)) is \( \frac{1}{2}\pi r^{2} \).

Substitute \( r = 6.25 \) and \( \pi = 3.14 \):

\( A=\frac{1}{2}\times3.14\times(6.25)^{2} \)

First, calculate \( (6.25)^{2}=39.0625 \)

Then, \( \frac{1}{2}\times3.14\times39.0625=1.57\times39.0625 = 61.328125 \) square units.

Now, let's solve for the semicircle labeled 10 (diameter 10 mm, using \( \pi = 3.14 \)).

Step 1: Find the radius

The radius \( r=\frac{10}{2}=5 \) mm.

Step 2: Calculate the perimeter of the semicircle

Using the formula \( P=\pi r + d \) (where \( d = 10 \) mm and \( r = 5 \) mm and \( \pi=3.14 \)):

\( P=3.14\times5+10 \)

\( 3.14\times5 = 15.7 \)

\( P=15.7 + 10=25.7 \) mm.

Step 3: Calculate the area of the semicircle

Using the formula \( A=\frac{1}{2}\pi r^{2} \) (where \( r = 5 \) mm and \( \pi = 3.14 \)):

\( A=\frac{1}{2}\times3.14\times(5)^{2} \)

\( (5)^{2}=25 \)

\( \frac{1}{2}\times3.14\times25 = 1.57\times25=39.25 \) square mm.

Answer:

For semicircle 9: Perimeter \( P = 32.125 \) units, Area \( A=61.328125 \) square units.

For semicircle 10: Perimeter \( P = 25.7 \) mm, Area \( A = 39.25 \) square mm.