6th Grade - Find The Circle's Area And Circumference

 
     
 
     
 
Newsletters:
 
     
 
 
6th
Geometry
Find the Circle's Area and Circumference
Understand the concept of a constant such as pi; know the formulas for the circumference and area of a circle.
Understand that pi is the ratio of the circumference of any circle to its diameter. Pi can be written using the symbol . Since pi is the ratio of c to d, it is always worth the same value. Sixth graders are required to round pi to the value of 3.14 in decimal form or 22/7 in fraction form. However, the value of pi is an approximation because pi is an infinite decimal. In fact, using a computer to get a closer estimation of pi, you’d get 3.14159265358979323846.
 

Sample Problems

(1)

A hat has a diameter of 6 inches. Which formula could be used to find the area of the hat?

(a) A = 6 (b) A = 12 (c) A = 36

(c)

(2)

Which is the correct algebraic representation for the area of a circle?

(a) A = d (b) A = rr (c) A = r2

(b)

(3)

A can lid has a diameter of 12 cm. Write the formula that should be used to find the circumference of the can lid.

(C x 12)

(4)

A Frisbee has a radius of 4 in. Express algebraically the formula that should be used to solve for circumference. Express algebraically the formula that should be used to solve for circumference.

(C (r x 2) or C (4 x 2))

(5)

A car tire has radius of 12 inches. What is its diameter?

(24)

Learning Tips

(1)

Since a circle is a special shape, you cannot find its area the way you would with a polygon. Also, a circle does not have a perimeter; it has what is called the circumference. The circumference is the measure around the outside of a circle. Since the circle is so different, its formulas are different too. The formulas for area and circumference both use a symbol to represent pi. The symbol or pi is . Its rounded value is 3.14 as a decimal and 22/7 as a fraction equivalent. When solving a problem with other fractions, the fraction would be used. The decimal form of pi can be used when working with whole numbers and decimals. The formulas for circles are as follows:

Circumference: C = d (This can be remembered by cd.)

Area: Circle: A = r 2 (This can be remembered by ar.)

In these formulas, d stands for diameter. The diameter of a circle is the measure from one edge of the circle to the opposite edge. The r stands for radius. The radius is the measure from the center of the circle to the outside edge. The radius of a circle is ½ the size of the diameter.

(2)

Since a circle is round, it is difficult to measure around the outside of it using a ruler. A hands-on activity simple activity can be done to find the circumference of a circle using a string and a ruler. First, draw or trace a circle (you can use different round cans and containers from the kitchen and try several). Next place a piece of string around the outside of the circle and cut it when both sides of the string touch. Now measure the string and you have the circumference. Since the circle is so different, its formulas are different too.

(3)

To help the visual and kinesthetic learner to understand why pi is almost equal to 3, you can take the hands on activity from above a step further. Have your child take the string used to measure the circumference of each circle and lay it on top of the circle it belongs to. Now, have your child stretch one end of the string across the diameter of the circle (from one edge to another across the middle). Cut the string where it touches the second edge and set the small piece of string to the side. Repeat this step for the longer half of the string. You will now have your circumference string cut into 3 diameter strings. You should see that each diameter string is about the same size. However, one string should be longer because pi is approximately equal to 3.14. Repeat these steps for different sized circles. The circumference will always be about 3 diameters. This is why pi is 3.14.

(4)

It is important for children to understand that the radius is one half the size of the diameter of a circle. This means the diameter is twice (2 times) the size of the radius. This is a constant. Students often confuse these terms. It helps some students to think of the sentence, “If you cut a circle in half it will die” and relate the word die to diameter. Children should practice turning a diameter into a radius by dividing by two and turning a radius into a diameter by multiplying by two. It would be a good idea for the visual learner to draw a circle and label the radius and diameter.

(5)

Children can create flashcards to help them memorize the formulas and vocabulary for this concept. Some recommended vocabulary terms are: radius, diameter, area formula, circumference formula, and pi.

Extra Help Problems

(1)

A circle has the diameter, r. Write a formula to show how to find the area of this circle.

(A r 2)

(2)

A circle has the diameter, d. Write a formula to show how to find the area of this circle.

(A (d/2) 2)

(3)

A circle has the diameter of 90. What formula could be used to find the area of a circle?

(A (90/2) 2)

(4)

A circle has the diameter of 90. What formula could be used to find the circumference of a circle?

(C 90)

(5)

A circle has the radius of 10. What formula could be used to find the circumference?

(C (10 x 2) )

(6)

A circle has the radius of 10. What formula could be used to find the area?

(A 102)

(7)

A circle has a diameter of 4 ¾. What formula could be used to find the area? What value for pi would be easiest to use? Explain.

(A (4-3/4 2) 2)

(8)

A circle has the radius of 3 ¼. What formula could be used to find the circumference?

(C (3-1/4 x 2))

(9)

A circle has the radius of 3 1/3. What formula could be used to find area?

(A 3-1/32)

(10)

A circle has a diameter of 5-2/3. What formula could be used to find circumference? What value for pi would be easiest to use? Explain.

(C d or C x 5-2/3 use 22/7 as the value for pi to keep the answer in fraction form.)

(11)

A circle has the diameter of 4.56. Express algebraically how to you could solve to find area. Which value for pi would be easiest to use? Explain.

(A r 2 or A (4.56/2) 2 use 3/14 to keep the answer in decimal form.)

(12)

A circle has the radius of 2.34. Express algebraically how to you could solve to find circumference. Which value for pi would be easiest to use? Explain.

(C (2.34 x 2) )

(13)

Will wants to make a dodge ball court with a diameter of 10 feet. How could he determine the circumference of the court? Show the formula and explain.

(C 10)

(14)

Jane wants to cover the outside rim of her lampshade with red ribbon. The radius of her lampshade is 4 inches. How could she determine how much ribbon she needs? Show the formula and explain.

(C 8, if the radius is 4, then the diameter is 8.)

(15)

A bike tire has a radius of 14 inches. James wants to cover his spokes and the inside of the tire with a decorative paper. How would James determine how much paper would be needed to fill the inside of the tire? Show the formula.

(A 142)

(16)

Cody’s water bottle base has a radius of 12 cm. He wants to use this information to calculate the circumference. What must he do before using the formula for circumference?

(Change the radius into the diameter by multiplying by 2. The diameter is 24.)

(17)

Jacenia has a circular compact with a broken mirror. It has a diameter of 3 inches. She wants to calculate the area of the case so that she can buy a mirror that fits inside. What must she do before she can use the formula for area?

(Change the diameter in to the radius by dividing by 2. The radius is 1.5.)

(18)

Write an expression that can be used to find the area of a circular bath mat with a radius of 13 in.

(A 132)

(19)

Write an expression that can be used to find the circumference of a CD with a radius of 5 ½ centimeters.

(C (5-1/2 x 2))

(20)

Write an expression that can be used to find the circumference of a trampoline with a diameter of 15 feet.

(C 15)

 

Related Games

 
 

Copyright ©2009 Big Purple Hippos, LLC