Question

Question:- A sector is cut from a circle of radius 21 cm . the angle of the sector is 150°. find the length of its arc and area.

Answer:- ?????
( i am so weak at math , can anybody tell me some tips to do math easily my board exams r coming ) ​

Answer 1

To calculate the length of the arc and the area of the sector, we can use the formulas:

1. Length of the arc (L):

L = (θ/360°) * 2πr

2. Area of the sector (A):

A = (θ/360°) * πr^2

where:

• - θ is the angle of the sector in degrees (150° in this case),
• - r is the radius of the circle (21 cm).

Now let's calculate the length of the arc and the area of the sector :

To find the length of the arc (L), we substitute the given values into the formula:

`\quad\quad\sf\:L = \left((150°)/(360°)\right) * 2\pi * 21 \, \text{cm} \\`

To find the area of the sector (A), we use the formula:

`\quad\quad\sf\:A = \left((150°)/(360°)\right) * \pi * (21 \, \text{cm})^2 \\`

Simplifying the calculations, we get:

`\quad\quad\sf\:L = \left((5)/(12)\right) * 2\pi * 21 \, \text{cm} \\`
`\\`

`\quad\quad\sf\:A = \left((5)/(12)\right) * \pi * (21 \, \text{cm})^2 \\`

Now you can substitute the numerical values and compute the results using a calculator.

`\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}`

♥️
`\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}`