Circles Review

Vocabulary

100

What is the name for the width of a circle?

Diameter

200

What is the name for the distance from the centre to the outside of a circle?

Radius

300

What is the name for the amount of space inside of a circle?

Area

400

What is the word that describes the perimeter, or distance around, a circle?

Circumference

500

What term represents the exact ratio of circumference to diameter? (Hint: The number is approximately 3)

Pi

Circumference

100

Find the circumference:

d = 6 m

C = pi x d
   = 3.14 x 6
   = 18.84 m

200

Find the circumference:

r = 10 cm

C = pi x d
   = 3.14 x 20      (r x 2 = 20)
   = 62.8 cm

300

Find the circumference:

Width = 21 m

C = pi x d
   = 3.14 x 21
   = 65.94 m

400

Use circumference to find the diameter.

C = 47.1 cm

C = pi x d   -->   C ÷ pi = d

47.1 ÷ 3.14 = 15
               d = 15 cm

500

Use circumference to find the radius.

C = 100.48 km

C = pi x d    -->    C ÷ pi = d

100.48 ÷ 3.14 = 32
                   d = 32
  d ÷ 2 = r
32 ÷ 2 = 16
        r = 16
      

Area

100

Find the area:

r = 13 mm

A = pi x r²
   = 3.14 x 13²
   = 3.14 x 169
   = 530.66 mm

200

Find the area:

d = 18 cm

A = pi x r²
   = 3.14 x 9²     (d ÷ 2 = 9)
   = 3.14 x 81
   = 254.34 cm

300

Find the area: 

Width = 5 m

A = pi x r²
   = 3.14 x 2.5²   (d ÷ 2 = 2.5)
   = 3.14 x 6.25
   = 19.625 m

400

Use area to find the radius:

A = 78.5 km²

A = pi x r²   --->   A ÷ pi = r²

78.5 ÷ 3.14 = r²

25 = r²

I know that 5 is the square root of 25.
r = 5

500

Use area to find the diameter:

A = 314 m

A = pi x r²     --->    A ÷ pi = r²

314 ÷ 3.14 = r²
           100 = r²
I know that 10 is the square root of 100.
             r = 10
If r = 10, then the d = 20. (r x 2 = d)

Word Problems

100

A circular drum is 19 cm wide. What is the distance around the drum?

Distance around = circumference

C = pi x d
   = 3.14 x 19
   = 59.66

The distance around the drum is 59.66cm.

200

A Tim Horton's cup is 12 cm wide. How much space does it take up on the table?

How much space = area

A = pi x r²
   = 3.14 x 6²   (d ÷ 2 = 6)
   = 3.14 x 36
   = 113.04

The cup takes up 113.04 cm² on the table.

300

A pond is in the shape of a circle. If you walked around the pond, you would have traveled 376.8 m. How wide is the pond?

How wide = diameter
Walked around = circumference

C = pi x d   --->   C ÷ pi = d
376.8 ÷ 3.14 = 120
                 d = 120

The pond is 120 m wide.

400

A hand (which is 15 cm long) on a clock travels around in a circle, one rotation every minute. How far does it travel in 4 minutes?

Length of the hand = radius = 15 cm
Distance around = circumference

C = pi x d
   = 3.14 x 30   (r x 2 = 30)
   = 94.2 cm
It travels 94.2 cm every minute.
Four minutes:   94.2 x 4 = 376.8 cm
In 4 minutes, the hand travels 376.8 cm.

500

A pizza is 24 inches wide. The chef knows they need 2 tablespoon of cheese for every square inch (in²) of pizza. How many tablespoons of cheese is needed for this pizza?

Square inches (in²)= area

A = pi x r²
   = 3.14 x 12²   (d ÷ 2 = 12)
   = 3.14 x 144
   = 452.16 in²

The pizza is 452.16 in². The chef needs 2 tablespoons of cheese for each in².

452.16 x 2 = 904.32
The chef needs 904.32 tablespoons of cheese for this pizza.

Random!

100

Write the formula for circumference.

C = pi x d

200

Write the formula for area.

A = pi x r²

300

Write a formula, or explain how you would FIND diameter, if you have the circumference.

d = C ÷ pi

You can divide circumference by pi, to find the diameter.

400

Write the symbol for pi.

(Must check for pi symbol)

500

Find 2 mistakes, and explain.

d = 8 m

A = pi x r²
   = 3.14 x 64
   = 200.96 m

1:   d was used instead of r.
      A = 3.14 x 4² (not 8²)
         = 3.14 x 16
         = 50.24

2:   The final answer should have units squared.
     m²