Math: Perimeter and Area of Circle Class 7

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Questions and Answers

What is the formula to calculate the circumference of a circle?

C = 2πr (correct)

C = 2r

C = πr^2

C = 3.14r

What is the relationship between the diameter and radius of a circle?

Diameter = 2r (correct)

Diameter = r/2

Diameter = r^2

Diameter = πr

Which formula is used to calculate the area of a circle?

Area = πr^2 (correct)

Area = πr

Area = 2πr

Area = 2r^2

If the diameter of a circle is 10 units, what is the radius?

5 units Signup and view all the answers

What does 'Circumference' refer to in relation to a circle?

The distance around the circle's edge Signup and view all the answers

Which of the following is equivalent to the formula for calculating the circumference of a circle?

$2 * r * π$ Signup and view all the answers

If a circle has a circumference of $16π$ units, what is the radius of the circle?

$8$ units Signup and view all the answers

What would be the diameter of a circle with an area of $144π$ square units?

$24$ units Signup and view all the answers

If a circle has an area of $100π$ square units, what is its circumference?

$40π$ units Signup and view all the answers

For a circle with a radius of $6$ cm, what is its approximate area in square centimeters?

$113.1$ square cm Signup and view all the answers

What is the relationship between the circumference and diameter of a circle?

$C = 2D$ Signup and view all the answers

If a circle has a circumference of $30π$ units, what would be its diameter?

$15$ units Signup and view all the answers

An area of $196π$ square units corresponds to what radius in centimeters for a circle?

$14$ cm Signup and view all the answers

If a circle has a diameter of $18$ cm, what is its approximate area in square centimeters?

$254.34$ square cm Signup and view all the answers

What is the approximate circumference in centimeters of a circle with an area of $36π$ square units?

$24$$ Signup and view all the answers

What is the relationship between the area of a sector of a circle and the central angle?

The area is directly proportional to the central angle Signup and view all the answers

If the radius of a circle is doubled, how does the circumference change?

It doubles Signup and view all the answers

What happens to the area of a circle if both the radius and diameter are doubled?

It quadruples Signup and view all the answers

How does changing the value of pi affect the calculation of the circumference and area of a circle?

Both circumference and area change proportionally Signup and view all the answers

In the context of circles, what is the relationship between the circumference and the diameter?

The circumference is equal to the diameter multiplied by $π$ Signup and view all the answers

If a circle has a sector area of $24π$ square units and the angle of the sector is $90$ degrees, what is the radius of the circle?

$4$ units Signup and view all the answers

A circle has a radius of $10$ cm. If the diameter is doubled, what would be the new circumference of the circle?

$80π$ units Signup and view all the answers

Study Notes

Math: Perimeter and Area of Circle Class 7

Welcome to a brief exploration of circles, focusing on their perimeter (circumference) and area. In this educational article, we'll delve into the important mathematical concepts, formulas, and examples relevant to seventh-grade students.

Circumference of a Circle

The circumference of a circle is the distance around the circle's edge. It's an essential measurement in geometry, and its formula is:

C = 2πr

Here, C represents circumference, π (pi) is a mathematical constant (approximately 3.14159), and r is the radius.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle's edge. Technically, a circle has only one radius, but we'll often see "radius" and "radius of a circle" used interchangeably.

Diameter of a Circle

The diameter of a circle is the straight-line distance between two opposite points on the circle's edge. The diameter is twice the length of the radius:

Diameter = 2r

Area of a Circle

The area of a circle enclosed by a given circumference is a valuable measurement in geometry. The formula for the area of a circle is:

Area = πr^2

Here, Area represents the area of the circle, and r is the radius of the circle.

Finding Circumference and Area

To find the circumference and area of a circle, use the following steps:

Identify the diameter of the circle.
Find the radius by dividing the diameter by 2.
Calculate the circumference using the formula C = 2πr.
Calculate the area using the formula Area = πr^2.

Example 1: Circumference

Suppose the diameter of a circle is 10 cm.

First, find the radius: Radius = Diameter / 2 = 10 / 2 = 5 cm

Then, calculate the circumference: Circumference = 2 * π * r = 2 * 3.14159 * 5 cm ≈ 31.4159 cm

Example 2: Area

Suppose the diameter of a circle is 5 cm.

First, find the radius: Radius = Diameter / 2 = 5 / 2 = 2.5 cm

Then, calculate the area: Area = π * r^2 = 3.14159 * (2.5 cm)^2 ≈ 19.6249 cm²

Conclusion

Circles are fascinating shapes that emerge in various fields of mathematics, science, and engineering. By understanding the concepts of circumference and area, you'll be well-equipped to explore geometric problems and discover new applications of mathematical principles.

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Description

Learn about the perimeter (circumference) and area of circles, including formulas and examples tailored for seventh-grade students. Explore concepts like radius, diameter, circumference, and area, and practice calculating these crucial measurements for circles.