Question

color by number
directions: solve each problem. remember to label your answers with the correct units. (the labels will not be part of your answer, but you should include them in your answering work.) then find the answer number on the coloring sheet and color it with the color given for that item. use 3.14 for π.

1. the circumference of a circle is 7.85 feet. what is the diameter?

color the answer: purple

1. cathy is making a banner for a science project. the radius of the banner is 3.8 inches. how long will the banner be?

color the answer: yellow

1. find the area of a circle with a 6 - cm diameter.

color the answer: blue

1. find the circumference of a circle with a 2.5 - inch diameter.

color the answer: brown

1. the circumference of a wheel is 9.42 feet. what is the diameter of the wheel?

color the answer: green

1. find the area of a circle with a 1.5 - cm radius.

color the answer: purple

1. the circumference of a circle is 27.475 inches. what is the circle’s radius?

color the answer: purple

1. find the area of a circle that has a circumference of 25.12 meters.

color the answer: blue

1. paul needs a pizza with a 6 - inch diameter. what will be the circumference of the pizza?

color the answer: brown

1. the radius of the bottom of tom’s champagne is 0.5 inches. what is the area of the bottom?

color the answer: green

1. mikey is making a model clock and is using a string border for it. the radius of the clock is 1.75 inches. how long is the border?

color the answer: purple

1. find the circumference of a circle with a 4.75 - cm radius.

color the answer: purple

1. find the area of a circle with a 5 - cm diameter.

color the answer: blue

1. find the circumference of a circle with a 4 - inch diameter.

color the answer: yellow

1. ben draws a circle with a circumference of 4.71 inches. what is the radius of the circle?

color the answer: pink

1. the circumference of a circle is 1.57 inches. what is the diameter?

color the answer: green

1. max bought a circular carpet for his room. its area is 78.5 feet². what is the radius of the carpet?

color the answer: blue

1. the circumference of a circle is 9.994 inches. what is the diameter?

color the answer: yellow

1. find the area of a circle with a 1 - cm radius.

color the answer: purple

1. find the circumference of a circle with a 6.25 - inch radius.

color the answer: green

Explanation:

To solve these circle - related problems, we use the formulas for the circumference (\(C = \pi d\) or \(C = 2\pi r\)) and area (\(A=\pi r^{2}\)) of a circle, where \(d\) is the diameter, \(r\) is the radius, and we use \(\pi\approx3.14\) or \(\pi=\frac{22}{7}\) as needed. Let's take a few problems as examples:

Problem 1: Find the circumference of a circle with a 1 - inch radius.

Step 1: Recall the formula for circumference

The formula for the circumference of a circle when the radius \(r\) is known is \(C = 2\pi r\). Here, \(r = 1\) inch and we take \(\pi\approx3.14\).

Step 2: Substitute the values into the formula

Substitute \(r = 1\) and \(\pi\approx3.14\) into \(C = 2\pi r\). We get \(C=2\times3.14\times1\).

Step 3: Calculate the result

\(2\times3.14\times1 = 6.28\) inches.

Problem 2: Find the area of a circle with a 5 - cm diameter.

Step 1: Find the radius

The radius \(r\) is half of the diameter \(d\). Given \(d = 5\) cm, so \(r=\frac{d}{2}=\frac{5}{2}=2.5\) cm.

Step 2: Recall the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), and we take \(\pi\approx3.14\).

Step 3: Substitute the values into the formula

Substitute \(r = 2.5\) cm and \(\pi\approx3.14\) into \(A=\pi r^{2}\). We get \(A = 3.14\times(2.5)^{2}\).

Step 4: Calculate the result

First, calculate \((2.5)^{2}=6.25\). Then, \(3.14\times6.25 = 19.625\) \(cm^{2}\).

Problem 3: The circumference of a circle is 1.57 inches. What is the diameter?

Step 1: Recall the formula for circumference

The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter and \(\pi\approx3.14\).

Step 2: Solve for \(d\)

We know that \(C = 1.57\) inches and \(\pi\approx3.14\). From \(C=\pi d\), we can re - arrange the formula to \(d=\frac{C}{\pi}\).

Step 3: Substitute the values into the formula

Substitute \(C = 1.57\) inches and \(\pi\approx3.14\) into \(d=\frac{C}{\pi}\). We get \(d=\frac{1.57}{3.14}\).

Step 4: Calculate the result

\(\frac{1.57}{3.14}=0.5\) inches.

For each of the problems in the worksheet, we can follow similar steps using the appropriate formula (circumference or area formula) and substituting the given values of radius or diameter to find the required quantity (circumference, area, radius, or diameter).

Answer:

To solve these circle - related problems, we use the formulas for the circumference (\(C = \pi d\) or \(C = 2\pi r\)) and area (\(A=\pi r^{2}\)) of a circle, where \(d\) is the diameter, \(r\) is the radius, and we use \(\pi\approx3.14\) or \(\pi=\frac{22}{7}\) as needed. Let's take a few problems as examples:

Problem 1: Find the circumference of a circle with a 1 - inch radius.

Step 1: Recall the formula for circumference

The formula for the circumference of a circle when the radius \(r\) is known is \(C = 2\pi r\). Here, \(r = 1\) inch and we take \(\pi\approx3.14\).

Step 2: Substitute the values into the formula

Substitute \(r = 1\) and \(\pi\approx3.14\) into \(C = 2\pi r\). We get \(C=2\times3.14\times1\).

Step 3: Calculate the result

\(2\times3.14\times1 = 6.28\) inches.

Problem 2: Find the area of a circle with a 5 - cm diameter.

Step 1: Find the radius

The radius \(r\) is half of the diameter \(d\). Given \(d = 5\) cm, so \(r=\frac{d}{2}=\frac{5}{2}=2.5\) cm.

Step 2: Recall the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), and we take \(\pi\approx3.14\).

Step 3: Substitute the values into the formula

Substitute \(r = 2.5\) cm and \(\pi\approx3.14\) into \(A=\pi r^{2}\). We get \(A = 3.14\times(2.5)^{2}\).

Step 4: Calculate the result

First, calculate \((2.5)^{2}=6.25\). Then, \(3.14\times6.25 = 19.625\) \(cm^{2}\).

Problem 3: The circumference of a circle is 1.57 inches. What is the diameter?

Step 1: Recall the formula for circumference

The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter and \(\pi\approx3.14\).

Step 2: Solve for \(d\)

We know that \(C = 1.57\) inches and \(\pi\approx3.14\). From \(C=\pi d\), we can re - arrange the formula to \(d=\frac{C}{\pi}\).

Step 3: Substitute the values into the formula

Substitute \(C = 1.57\) inches and \(\pi\approx3.14\) into \(d=\frac{C}{\pi}\). We get \(d=\frac{1.57}{3.14}\).

Step 4: Calculate the result

\(\frac{1.57}{3.14}=0.5\) inches.

For each of the problems in the worksheet, we can follow similar steps using the appropriate formula (circumference or area formula) and substituting the given values of radius or diameter to find the required quantity (circumference, area, radius, or diameter).