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 = 2Ï€r (correct)
  • C = 2r
  • C = Ï€r^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 = Ï€r

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

  • Area = Ï€r^2 (correct)
  • Area = Ï€r
  • Area = 2Ï€r
  • Area = 2r^2

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

<p>5 units (C)</p> Signup and view all the answers

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

<p>The distance around the circle's edge (C)</p> Signup and view all the answers

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

<p>$2 * r * π$ (A)</p> Signup and view all the answers

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

<p>$8$ units (A)</p> Signup and view all the answers

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

<p>$24$ units (A)</p> Signup and view all the answers

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

<p>$40Ï€$ units (D)</p> Signup and view all the answers

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

<p>$113.1$ square cm (C)</p> Signup and view all the answers

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

<p>$C = 2D$ (A)</p> Signup and view all the answers

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

<p>$15$ units (D)</p> Signup and view all the answers

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

<p>$14$ cm (B)</p> Signup and view all the answers

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

<p>$254.34$ square cm (B)</p> Signup and view all the answers

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

<p>$24$$ (B)</p> Signup and view all the answers

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

<p>The area is directly proportional to the central angle (A)</p> Signup and view all the answers

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

<p>It doubles (A)</p> Signup and view all the answers

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

<p>It quadruples (C)</p> Signup and view all the answers

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

<p>Both circumference and area change proportionally (C)</p> Signup and view all the answers

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

<p>The circumference is equal to the diameter multiplied by $Ï€$ (C)</p> Signup and view all the answers

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

<p>$4$ units (B)</p> 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?

<p>$80Ï€$ units (C)</p> 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 = 2Ï€r

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:

  1. Identify the diameter of the circle.
  2. Find the radius by dividing the diameter by 2.
  3. Calculate the circumference using the formula C = 2Ï€r.
  4. 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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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.

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