Educational worksheet for calculating the radius and diameter of circles.
A worksheet titled "Radius and Diameter" with diagrams of circles showing radius and diameter measurements, used for calculating the radius and diameter of each circle.
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Show Answer Key & Explanations
Step-by-step solution for: Circle Circumference Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Circle Circumference Worksheet
To solve this worksheet, we need to understand the relationship between the radius and the diameter of a circle.
Key Concepts:
1. Radius ($r$): The distance from the center of the circle to the edge (the outer line).
2. Diameter ($d$): The distance across the circle, passing through the center. It cuts the circle in half.
3. The Rule: The diameter is always double the radius ($d = 2 \times r$), and the radius is always half the diameter ($r = d / 2$).
Now, let's look at each part of the worksheet:
* Part a: The image shows a line from the center to the edge labeled $8\text{ mm}$. This is the radius.
* Radius = $8\text{ mm}$
* Diameter = $8 \times 2 = 16\text{ mm}$
* Part b: The image shows a line all the way across the circle labeled $19\text{ cm}$. This is the diameter.
* Diameter = $19\text{ cm}$
* Radius = $19 / 2 = 9.5\text{ cm}$
* Part c: The image shows a line from the center to the edge labeled $4\text{ m}$. This is the radius.
* Radius = $4\text{ m}$
* Diameter = $4 \times 2 = 8\text{ m}$
* Part d: The image shows a line all the way across the circle labeled $14\text{ km}$. This is the diameter.
* Diameter = $14\text{ km}$
* Radius = $14 / 2 = 7\text{ km}$
* Part e: The image shows a line from the center to the edge labeled $11\text{ m}$. This is the radius.
* Radius = $11\text{ m}$
* Diameter = $11 \times 2 = 22\text{ m}$
* Part f: The image shows a line all the way across the circle labeled $20\text{ ft}$. This is the diameter.
* Diameter = $20\text{ ft}$
* Radius = $20 / 2 = 10\text{ ft}$
* Part g: The image shows a line all the way across the circle labeled $24\text{ km}$. This is the diameter.
* Diameter = $24\text{ km}$
* Radius = $24 / 2 = 12\text{ km}$
* Part h: The image shows a line from the center to the edge labeled $1\text{ cm}$. This is the radius.
* Radius = $1\text{ cm}$
* Diameter = $1 \times 2 = 2\text{ cm}$
* Part i: The image shows a line all the way across the circle labeled $19\text{ cm}$. This is the diameter.
* Diameter = $19\text{ cm}$
* Radius = $19 / 2 = 9.5\text{ cm}$
* Part j: The image shows a line from the center to the edge labeled $1\text{ m}$. This is the radius.
* Radius = $1\text{ m}$
* Diameter = $1 \times 2 = 2\text{ m}$
* Part k: The image shows a line all the way across the circle labeled $12\text{ cm}$. This is the diameter.
* Diameter = $12\text{ cm}$
* Radius = $12 / 2 = 6\text{ cm}$
* Part l: The image shows a line all the way across the circle labeled $50\text{ mm}$. This is the diameter.
* Diameter = $50\text{ mm}$
* Radius = $50 / 2 = 25\text{ mm}$
* Part m (Word Problem): "John has a round swimming pool. The distance from the center of the pool to the edge is $3\text{ meters}$. What is the diameter of John's pool?"
* The "distance from the center to the edge" is the definition of the radius. So, $r = 3\text{ meters}$.
* To find the diameter, we multiply the radius by $2$.
* Calculation: $3 \times 2 = 6$.
* Answer: $6\text{ meters}$.
Final Answer:
a. radius = $8\text{ mm}$, diameter = $16\text{ mm}$
b. radius = $9.5\text{ cm}$, diameter = $19\text{ cm}$
c. radius = $4\text{ m}$, diameter = $8\text{ m}$
d. radius = $7\text{ km}$, diameter = $14\text{ km}$
e. radius = $11\text{ m}$, diameter = $22\text{ m}$
f. radius = $10\text{ ft}$, diameter = $20\text{ ft}$
g. radius = $12\text{ km}$, diameter = $24\text{ km}$
h. radius = $1\text{ cm}$, diameter = $2\text{ cm}$
i. radius = $9.5\text{ cm}$, diameter = $19\text{ cm}$
j. radius = $1\text{ m}$, diameter = $2\text{ m}$
k. radius = $6\text{ cm}$, diameter = $12\text{ cm}$
l. radius = $25\text{ mm}$, diameter = $50\text{ mm}$
m. answer: $6\text{ meters}$
Key Concepts:
1. Radius ($r$): The distance from the center of the circle to the edge (the outer line).
2. Diameter ($d$): The distance across the circle, passing through the center. It cuts the circle in half.
3. The Rule: The diameter is always double the radius ($d = 2 \times r$), and the radius is always half the diameter ($r = d / 2$).
Now, let's look at each part of the worksheet:
* Part a: The image shows a line from the center to the edge labeled $8\text{ mm}$. This is the radius.
* Radius = $8\text{ mm}$
* Diameter = $8 \times 2 = 16\text{ mm}$
* Part b: The image shows a line all the way across the circle labeled $19\text{ cm}$. This is the diameter.
* Diameter = $19\text{ cm}$
* Radius = $19 / 2 = 9.5\text{ cm}$
* Part c: The image shows a line from the center to the edge labeled $4\text{ m}$. This is the radius.
* Radius = $4\text{ m}$
* Diameter = $4 \times 2 = 8\text{ m}$
* Part d: The image shows a line all the way across the circle labeled $14\text{ km}$. This is the diameter.
* Diameter = $14\text{ km}$
* Radius = $14 / 2 = 7\text{ km}$
* Part e: The image shows a line from the center to the edge labeled $11\text{ m}$. This is the radius.
* Radius = $11\text{ m}$
* Diameter = $11 \times 2 = 22\text{ m}$
* Part f: The image shows a line all the way across the circle labeled $20\text{ ft}$. This is the diameter.
* Diameter = $20\text{ ft}$
* Radius = $20 / 2 = 10\text{ ft}$
* Part g: The image shows a line all the way across the circle labeled $24\text{ km}$. This is the diameter.
* Diameter = $24\text{ km}$
* Radius = $24 / 2 = 12\text{ km}$
* Part h: The image shows a line from the center to the edge labeled $1\text{ cm}$. This is the radius.
* Radius = $1\text{ cm}$
* Diameter = $1 \times 2 = 2\text{ cm}$
* Part i: The image shows a line all the way across the circle labeled $19\text{ cm}$. This is the diameter.
* Diameter = $19\text{ cm}$
* Radius = $19 / 2 = 9.5\text{ cm}$
* Part j: The image shows a line from the center to the edge labeled $1\text{ m}$. This is the radius.
* Radius = $1\text{ m}$
* Diameter = $1 \times 2 = 2\text{ m}$
* Part k: The image shows a line all the way across the circle labeled $12\text{ cm}$. This is the diameter.
* Diameter = $12\text{ cm}$
* Radius = $12 / 2 = 6\text{ cm}$
* Part l: The image shows a line all the way across the circle labeled $50\text{ mm}$. This is the diameter.
* Diameter = $50\text{ mm}$
* Radius = $50 / 2 = 25\text{ mm}$
* Part m (Word Problem): "John has a round swimming pool. The distance from the center of the pool to the edge is $3\text{ meters}$. What is the diameter of John's pool?"
* The "distance from the center to the edge" is the definition of the radius. So, $r = 3\text{ meters}$.
* To find the diameter, we multiply the radius by $2$.
* Calculation: $3 \times 2 = 6$.
* Answer: $6\text{ meters}$.
Final Answer:
a. radius = $8\text{ mm}$, diameter = $16\text{ mm}$
b. radius = $9.5\text{ cm}$, diameter = $19\text{ cm}$
c. radius = $4\text{ m}$, diameter = $8\text{ m}$
d. radius = $7\text{ km}$, diameter = $14\text{ km}$
e. radius = $11\text{ m}$, diameter = $22\text{ m}$
f. radius = $10\text{ ft}$, diameter = $20\text{ ft}$
g. radius = $12\text{ km}$, diameter = $24\text{ km}$
h. radius = $1\text{ cm}$, diameter = $2\text{ cm}$
i. radius = $9.5\text{ cm}$, diameter = $19\text{ cm}$
j. radius = $1\text{ m}$, diameter = $2\text{ m}$
k. radius = $6\text{ cm}$, diameter = $12\text{ cm}$
l. radius = $25\text{ mm}$, diameter = $50\text{ mm}$
m. answer: $6\text{ meters}$
Parent Tip: Review the logic above to help your child master the concept of circumference worksheets.
