6th Grade - Using Pi

Using Pi
Know common estimates of pi (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.
The value of pi can be represented as a decimal (3.14) or a fraction (22/7). Use the decimal estimate when solving problems with decimals and whole numbers (i.e. radius = 4.5). Use the fraction estimate of pi when working with problems involving fractions (i.e. radius = 5 1/4 ). A formula can be used to calculate the circumference or area of a circle. The formula for circumference is C = πd or C = 2 π r. The formula to be used to calculate the area of a circle is A = πr 2. Estimations of the circumference or area of a circle can be made using the formulas and knowing that pi is about 3. Calculate the actual circumference and/or area of a circle can be done using the correct formula and the common estimate for pi. Compare actual measurements with estimates to verify reasonableness of results.

Sample Problems


A circle has a diameter of 6 ¾ inches. What is the circumference of the circle?

(42.39 in.)


A circle has a radius of 6.75 inches. What is the area of the circle to the nearest whole number?

(143 cm 2 )


A can lid has a diameter of 9 cm. Use the correct formula to find the circumference of the can lid.

(28.26 cm)


A Frisbee has a radius of 4 in. Solve to find circumference.

(25.12 cm)


A car tire has diameter of 12 inches. Solve to find area.

(113.04 in. 2 )

Learning Tips


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.) This formula stands for Circumference (C) equals (=) pi () times diameter (d).

Area: Circle: A = r 2 (This can be remembered by making the ”ar” sound twice.) This formula stands for Area (A) equals (=) pi () times the radius squared (to the second power).

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.


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.


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. The diameter is the longest line that can cut a circle into parts. It cuts the circle in half, crossing through the center point. 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. He/she can thereby remember that the radius must be the smaller line. 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.


Often times, sixth graders are given a problem where they will need to convert radius into diameter to find circumference. For example, a problem could say, “The radius of a circle is 2 cm, find the circumference.” In order to solve this problem, the formula for circumference will need to be used (C = d). The problem, however, only give us the radius, “r”. Hence, “r” will need to be changed into “d”, diameter before the circumference can be found. Since the radius is ½ the side of the diameter and two diameters equal one radius, we simply need to multiply “r” by 2 to find “d”. So in the problem above since r = 2 and 2 x 2 = 4, then d = 4. So, to solve the problem we would not input our numbers into the formula, as follows.

C = d

C = 3.14 x 4

C = 12.56 cm


There are also times when diameter needs to be turned into radius to solve for area. Since, the area formula for a circle is A = r 2, a problem that asks us to solve to find the area of a circle that has a diameter of 10 cm will require converting diameter into radius. The diameter is twice the radius. Since the diameter is larger than the radius, we will need to divide by 2 to change the diameter into radius. So, 10 divided by 2 = 5. The radius of a circle with a diameter of 10 will have a radius of 5. So, r = 5 cm. We can used this information and the formula to find area, as shown below.

A = r 2

A = 3.14 x 52

A = 3.14 x 25

A = 78.5 cm2


It is very important that the order of operations be used when solving problems with formulas. This is especially true with finding the area of a circle, because the formula for finding the area of a circle has two operations (multiplication and exponents). The order of operations state that exponents must be solved before multiplication. Forgetting to solve for the exponent first will result in an incorrect solution.


Children that struggle with algebraic concepts may benefit from a more kinesthetic/visual approach to solving problems in the beginning. To provide this for them, you can draw a circle with one line through the middle to represent the diameter. In another color trace over half the diameter to show the radius. Now, use a sticky note to show either the value of the radius or diameter. Give your child a blank sticky note and have him/her fill in the value of the missing radius or diameter. Next, write out the formula you’d like to have your child solve. So for circumference you’d write out C = x d. (It is best show the operation symbol for struggling students.) On two sticky notes have the estimates for pi: 3.14 and 22/7. Have your child remove the sticky note from the circle that represents d, diameter and stick it on top of the d in the formula. Then, have your child take the pi sticky note that will be easiest to use with d and place it on top of the . Your child will be left with a problem with only one variable, C. He/she now simply needs to multiply the numbers on the sticky notes to find C. Now try the same thing, but use the area formula. Repeat this several times until your child feels comfortable substituting a value in for a variable.

Extra Help Problems


Solve for circumference.

d = 11 cm

(34.54 cm)


Solve for circumference.

d = 4 m

(12.56 m)


Solve for circumference.

d = 5.25 in.

(16.485 in)


Solve for circumference.

d = 2 ½ ft.

(7-6/7 ft.)


Solve for circumference.

d = 3 ¼ mm

(10-3/14 mm)


Solve for circumference.

r = 11 m

(69.08 m)


Solve for circumference.

r = 3.25 cm

(20.42 cm)


Solve for circumference.

r = 4 ¼ mm

(26-5/7 mm)


Solve for area.

r = 9 ft.

(254.34 ft. 2 )


Solve for area.

r = 25 mi

(1962.25 mi2 )


Solve for area. Round your answer to the nearest whole number.

r = 6.3 dm

(125 dm2 )


Solve for area.

r = 4 ½ yd

(63.585 yd2 )


Solve for area.

d = 10 ft

(78.15 ft2 )


Solve for area.

d = 9 in.

(63.585 in2 )


Solve for area.

d = 4 ½ cm



A ferris wheel has a diameter of 60 yards. What is the measure around the outside of the wheel?

(188.4 yd)


A merry-go-round has a radius of 35 feet. They would like to trim the outside edge of the circular base with colorful streamers. How many feet of streamers will they need?

(219.8 ft.)


Kristin would like to make circular drink coasters for her party. She has traced the circle from the base of the cup so that she can cover it in fabric. When she measured the diameter of the circle it was 4 inches. How much fabric will she need for each drink coaster?

(12.56 in.)


The top of a magician’s hat has a radius of 12 cm. The magician needs a new band to go around the outside of the hat. How long should the band be in order to fit around the hat without being too long?

(75.36 cm)


The top of a magician’s hat has a radius of 12 cm. The magician needs a new circular cut-out to fill the inside of this hat. What size should the circle be so that it fits the hat perfectly?

(452.16 cm2 )


Sadie is running for student body president and would like to hand out election buttons. She has a circle cut-out that has a diameter of 6 ½ centimeters. She wants to glue red, white and blue trim around the outside of each button. How much trim will she use per button? How much will she need to buy, if she plans on making 50 buttons?

(1,020.5 cm)


Sam is running for student body president. He is making 100 election buttons to gain support. He would like each button to have a circle with a radius of 7.25 cm. What will be the area of each button to the nearest cm?

(165 cm2 )


The netting on Eric’s trampoline has torn. He needs to replace the entire inside. Eric measured his trampoline and found that it had a diameter of 14 feet. How much netting does Eric need to buy to replace the inside?

(153.86 ft. 2 )


Naomi and her friends ordered a pizza. The radius of the pizza was 14 ½ inches. What was the measure of the crust?

(91.06 in.)


Naomi and her friends ordered a pizza. The radius of the pizza was 14 ½ inches. What was the measure of cheese?

(660.185 in. 2 )


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