Radius & Diameter
The radius of a circle is 10 mm. How long is the diameter?
20 mm
The diameter of a circle is 40 cm. What is the circumference?
Use 3.14 for pi. Round to the nearest tenth.
125.6 cm
The diameter of a circle is 6 inches. What is the area?
Use 3.14 for pi, and round to the nearest tenth.
28.3 in2
A hula hoop is 24 cm wide. What is the distance around the hula hoop?
C = 3.14d The hula hoop has a diameter of 24.
C = 3.14 x 24
C = 75.36
The distance around the hula hoop is 75.36 cm.
The second hand of a clock is 11 cm long. How far does the point of the minute hand travel in 30 seconds (half a minute)?
The minute hand will travel half of a rotation, so I need to know what half of the circumference is.
C = 3.14d The radius is 11, so the diameter is 22cm.
C = 3.14 x 22
= 69.08 cm
Half of C: 69.08 ÷ 2 = 34.54 cm
The point travels 34.54 cm in half of a minute.
The diameter of a circle is 18 cm. How long is the radius?
9 cm
The radius of a circle is 15 mm. What is the circumference?
Use 3.14 for pi, and round to the nearest tenth.
94.2 mm
The radius of a circle is 13 m. What is the area?
Use 3.14 for pi, and round to the nearest tenth.
530.7 m2
The minute hand on a wrist watch is 16 mm long. What is the distance the end of the minute hand travels, in one rotation?
C = 3.14d The radius of the circle is 16, so the diameter is 2-times that length: 32 mm.
C = 3.14 x 32
C = 100.48 mm
The end of the minute hand travels 100.48 mm in one rotation.
Describe the relationship between diameter and circumference.
The circumference is approximately 3-times the diameter. This explains why pi is a number that is slightly more than 3 (3.14 etc.)
The diameter is ______ the length of the radius.
- twice
- 2 times
- double
The diameter is 18.5 km. What is the circumference?
Use 3.14 for pi, and round to the nearest tenth.
58.1 km
The diameter of a circle is 19 km. What is the area?
Use 3.14 for pi, and round to the nearest tenth.
283.4 km2
The vase has a circular bottom, with a width of 4 inches. How much shelf space does the vase take up?
A = 3.14r2 The radius is half of the width, so r = 2.
= 3.14(2 x 2)
= 3.14 x 4
= 12.56 in2
The vase takes up 12.56 square inches on the shelf.
A box of cupcakes has 3 rows of 4 cupcakes. Each cupcake has a radius of 2.5 cm. How long and how wide should this box of cupcakes be?
Each cupcake is 5 cm wide, if the radius is 2.5
Each row has 4 cupcakes: 4 x 5 = 20 cm
There are 3 rows: 3 x 5 = 15 cm
The box should be 20 cm long and 15 cm wide.
The diameter is the ______ of a circle.
Width
The radius of a circle is 12.5 m. What is the circumference?
Use 3.14 for pi, and round to the nearest tenth.
78.5 m
The radius of a circle is 7.25 m. What is the area?
Use 3.14 for pi, and round to the nearest tenth.
165 m2
A circular walking path has a water fountain in the very centre of the circle, which is always 8 metres away from the path.
Mr. V ran 9 laps around the path. What distance did he run?
C = 3.14d The radius is 8, so the diameter is 16m
C = 3.14 x 8
C = 25.12 m 1 lap = 25.12 m
9 laps: 9 x 25.12 = 226.08
Mr. V ran 226.08 m.
A bagel is 6 inches wide. Ms. H slices it in half and toasts it. She spreads cream cheese over both halves (even covering the hole). Each square inch requires 2 teaspoons of cream cheese. How many teaspoons of cream cheese does she need?
Round the nearest whole teaspoon.
A = 3.14r2 The diameter is 6, so r = 3.
A of each slice: 3.14(3 x 3)
= 3.14 x 9
= 28.26 in2
2 slices: 28.26 x 2 = 56.52 in2 of cream cheese
Each square inch = 2 teaspoons
56.52 x 2 = 113.04
Ms. H needs 113 teaspoons (rounded) of cream cheese.
There are 3 bicycle tires laying in a row on the ground. The length of the entire row is 120cm.
What is the radius of 1 bicycle tire?
Each tire has a diameter of 40cm. [120 ÷ 3 = 40]
The radius of each tire is 20cm.
The circumference of a circle is 50.24 cm. What is the diameter?
50.24 = 3.14d
50.24 ÷ 3.14 = d
16 = d
The diameter is 16 cm.
The area of a circle is 1, 017.36 m2. What is the radius?
1017.36 = 3.14r2
1017.36 ÷ 3.14= r2
324 = r2
⎷324 = r (*square root*)
18 = r
The radius is 18 m.
There are 6 cylindrical bottles of paint on a shelf. Each bottle is 10 cm wide. How much space do they take up on the shelf?
A = 3.14r2 The diameter for 1 bottle is 10cm, so the radius is 5cm.
A = 3.14(5 x 5)
= 3.14 x 25
= 77.5 cm2 Each bottle takes up 77.5cm2.
6 bottles: 6 x 77.5 = 465 cm2
These bottles of paint take up 465 square cm of shelf space.
A cheerio is 10 mm wide, but the hole in it is 3mm wide. How much area does the cheerio take up on the spoon (not including the hole)?
I need to subtract the area of the hole, from the area of the circle made by the width of the cheerio. A = 3.14r2
A of cheerio: 3.14(5 x 5) Diameter is 10, r = 5
= 3.14 x 25
= 78.5 mm2
A of hole: 3.14(1.5 x 1.5) Diameter is 3, r = 1.5
= 3.14 x 2.25
= 7.065 mm2
78.5 - 7.065 = 71.435 mm2
The area that the cheerio takes up, without the hole, is 71.435 mm2.