If the radius of a circle is (2)/(3)+(1)/(7). Find the circumference, area and also find the area of (1)/(4)^("th ") of the circle.

Calculate Radius: Calculate the radius of the circle by adding the fractions 2/3 and 1/7. To add fractions, we need a common denominator. The least common multiple of 3 and 7 is 21. So we convert the fractions to have the same denominator and then add them. \[ \frac{2}{3} + \frac{1}{7} = \frac{2 \times 7}{3 \times 7} + \frac{1 \times 3}{7 \times 3} = \frac{14}{21} + \frac{3}{21} = \frac{14 + 3}{21} = \frac{17}{21} \]Calculate Circumference: Calculate the circumference of the circle using the formula $ C = 2\pi r $, where $ r $ is the radius. \[ C = 2\pi \times \frac{17}{21} \] \[ C = \frac{34\pi}{21} \]Calculate Area: Calculate the area of the circle using the formula $ A = \pi r^2 $, where $ r $ is the radius. \[ A = \pi \times \left(\frac{17}{21}\right)^2 \] \[ A = \pi \times \frac{289}{441} \] \[ A = \frac{289\pi}{441} \]Calculate 1/4 Area: Calculate the area of 1/4 of the circle by dividing the total area by 4. \[ \text{Area of 1/4 of the circle} = \frac{1}{4} \times \frac{289\pi}{441} \] \[ \text{Area of 1/4 of the circle} = \frac{289\pi}{441 \times 4} \] \[ \text{Area of 1/4 of the circle} = \frac{289\pi}{1764} \]

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If the radius of a circle is (2)/(3)+(1)/(7). Find the circumference, area and also find the area of (1)/(4)^("th ") of the circle.

If the radius of a circle is $\frac{2}{3} + \frac{1}{7}$ . Find the circumference, area and also find the area of $\frac{1}{4}^{\text {th }}$ of the circle.

View step-by-step help

Home

Math Problems

Algebra 2

Find trigonometric ratios using the unit circle

Full solution

Q. If the radius of a circle is

\frac{2}{3} + \frac{1}{7}

. Find the circumference, area and also find the area of

\frac{1}{4}^{\text {th }}

of the circle.

Calculate Radius: Calculate the radius of the circle by adding the fractions $2$ / $3$ and $1$ / $7$ . $\newline$ To add fractions, we need a common denominator. The least common multiple of $3$ and $7$ is $21$ . So we convert the fractions to have the same denominator and then add them. $\newline$ $\frac{2}{3} + \frac{1}{7} = \frac{2 \times 7}{3 \times 7} + \frac{1 \times 3}{7 \times 3} = \frac{14}{21} + \frac{3}{21} = \frac{14 + 3}{21} = \frac{17}{21}$
Calculate Circumference: Calculate the circumference of the circle using the formula $C = 2\pi r$ , where $r$ is the radius. $\newline$ $C = 2\pi \times \frac{17}{21}$ $\newline$ $C = \frac{34\pi}{21}$
Calculate Area: Calculate the area of the circle using the formula $A = \pi r^2$ , where $r$ is the radius. $\newline$ $A = \pi \times \left(\frac{17}{21}\right)^2$ $\newline$ $A = \pi \times \frac{289}{441}$ $\newline$ $A = \frac{289\pi}{441}$
Calculate $1$ / $4$ Area: Calculate the area of $1$ / $4$ of the circle by dividing the total area by $4$ . $\newline$ $\text{Area of 1/4 of the circle} = \frac{1}{4} \times \frac{289\pi}{441}$ $\newline$ $\text{Area of 1/4 of the circle} = \frac{289\pi}{441 \times 4}$ $\newline$ $\text{Area of 1/4 of the circle} = \frac{289\pi}{1764}$