Find the circumference. Use π=3.14π=3.14.

65.94cm⁡65.94\operatorname{\mathrm{cm}}65.94cm

21cm⁡21\operatorname{\mathrm{cm}}21cm

10.5cm⁡10.5\operatorname{\mathrm{cm}}10.5cm

32.97cm⁡32.97\operatorname{\mathrm{cm}}32.97cm

Find the area of the circle. Use π=227\pi=\frac{22}{7} and simplify.

154mm⁡2154\operatorname{\mathrm{mm}}^2154mm2

22mm⁡222\operatorname{\mathrm{mm}}^222mm2

44cm⁡244\operatorname{\mathrm{cm}}^244cm2

616cm⁡2616\operatorname{\mathrm{cm}}^2616cm2

Find the area of the circle. Use π=227\pi=\frac{22}{7} and simplify.

5507\frac{550}{7}7550 $$m^{2}$$

2207\frac{220}{7}7220 $$m^{2}$$

11007\frac{1100}{7}71100 $$m^{2}$$

1107\frac{110}{7}7110 $$m^{2}$$

9. Geometry

Circles

9. Geometry

Circles: 동영상 및 연습문제

비디오 강의 워크시트

주제 요약

Circles are measured using the radius, diameter, circumference, and area. The radius is the distance from the center to the edge, and the diameter goes across the circle through the center, so $d=2r$ . The circumference is the distance around the circle and is found with $C=\pi d$ or $C=2\pi r$ . The constant pi relates circumference to diameter and is often approximated by $3.14$ or $\frac{22}{7}$.

The area of a circle is found with $A=\pi r^2$ . This formula can be understood by rearranging circle wedges into a shape like a parallelogram with base $\pi r$ and height $r$. When a diameter is given, find the radius first before using the area formula. Area is written in square units, and parts of circular figures, such as a half circle or a ring-shaped region, can be found by combining or subtracting circle areas as needed.

개념

Circumference of a Circle

영상 길이:

워크시트로 더 똑똑하게 공부하세요.

각 영상을 인쇄 가능한 워크시트로 따라 하세요

문제

What is the radius of the following circle?

$5.2$\operatorname{\mathrm{mi}$}$

$2.6$\operatorname{\mathrm{mi}$}$

$16.3$\operatorname{\mathrm{mi}$}$

$8.2$\operatorname{\mathrm{mi}$}$

문제

Find the circumference. Use $pi equals 3.14$ .

$21$\operatorname{\mathrm{cm}$}$

$10.5$\operatorname{\mathrm{cm}$}$

$65.94$\operatorname{\mathrm{cm}$}$

$32.97$\operatorname{\mathrm{cm}$}$

문제

Find the circumference. Use $pi equals 3.14$ .

$34.54$ yd

$17.27$ yd

$11$ yd

$5.5$ yd

예시

Circumference of a Circle Example 1

영상 길이:

개념

Area of a Circle

영상 길이:

문제

Find the area of the circle. Use $π = \frac{22}{7}$ and simplify.

$22$\operatorname{\mathrm{mm}$}^2$

$154$\operatorname{\mathrm{mm}$}^2$

$44$\operatorname{\mathrm{cm}$}^2$

$616$\operatorname{\mathrm{cm}$}^2$

문제

Find the area of the circle. Use $π = \frac{22}{7}$ and simplify.

$\frac{550}{7}$ m²

$\frac{220}{7}$ m²

$\frac{1100}{7}$ m²

$\frac{110}{7}$ m²

예시

Area of a Circle Example 2

영상 길이:

예시

Area of a Circle Example 3

영상 길이:

학생들이 이 주제에 대해 묻는 질문은 다음과 같습니다:

The circumference of a circle is the distance around its edge. It is given by the formula $C = π d$ , where $d$ is the diameter of the circle. Since the diameter is twice the radius ( $d = 2 r$ ), the formula can also be written as $C = 2 π r$ . This relationship comes from measuring how many times the diameter fits around the circle's edge, which is approximately 3.14159 times, a value known as pi ( $π$ ). Pi is an irrational number, meaning it has an infinite, non-repeating decimal expansion. For practical calculations, pi is often approximated as 3.14 or $\frac{22}{7}$ . Understanding this formula helps in calculating the perimeter of circular shapes accurately.

The area of a circle is calculated using the formula $A = π r^{2}$ , where $r$ is the radius. This formula can be understood by dividing the circle into many small wedges, then rearranging these wedges to form a shape resembling a parallelogram. The base of this parallelogram is half the circumference, which is $π r$ , and the height is the radius $r$ . The area of a parallelogram is base times height, so multiplying these gives $π r \cdot r$ or $π r^{2}$ . This geometric interpretation explains why the formula accurately represents the area inside a circle.

The radius of a circle is half the length of its diameter. If you are given the diameter $d$ , you can find the radius $r$ using the formula $r = \frac{d}{2}$ . This is because the diameter is defined as the distance across the circle passing through its center, which is exactly twice the radius. Knowing the radius is essential for calculating other properties of the circle, such as its circumference and area.

Pi ( $π$ ) is an irrational number approximately equal to 3.14159265..., and it never ends or repeats. For practical purposes, pi is often approximated as 3.14 when using decimals or as the fraction $\frac{22}{7}$ . These approximations simplify calculations of circumference and area without significantly affecting accuracy for most applications. For example, when calculating circumference, you might use $C = 3.14 \cdot d$ or $C = \frac{22}{7} \cdot d$ depending on the context.

When the radius $r$ of a circle is known, the circumference $C$ can be calculated using the formula $C = 2 π r$ . This formula comes from the relationship between the diameter and radius, where the diameter is twice the radius ( $d = 2 r$ ). Since circumference is $C = π d$ , substituting $d$ with $2 r$ gives the formula involving the radius. Using this formula, you multiply 2, pi, and the radius to find the total distance around the circle.