Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
Share
Notifications

View all notifications

The Area of a Sector of a Circle of 6 Cm Radius is 15 π Sq.Cm. Find the Measure of the Arc and Length of the Arc Corresponding to the Sector. - Geometry

Login
Create free account


      Forgot password?

Question

The area of a sector of a circle of 6 cm radius is 15 \[\pi\] sq.cm. Find the measure of the arc and length of the arc corresponding to the sector.

Solution

The radius of the sector, r = 6 cm
Let the measure of the arc be θ and the length of the arc corresponding to the sector be l cm. 
Area of the sector = 15 \[\pi\] cm2         (Given)

\[\therefore \frac{1}{2}lr = 15\pi\]
\[ \Rightarrow \frac{1}{2} \times l \times 6 = 15\pi\]
\[ \Rightarrow l = \frac{15\pi}{3} = 5\pi \text{ cm} \]

Length of the arc = \[5\pi \text{ cm} \]

\[\therefore \frac{\theta}{360°} \times 2\pi r = 5\pi\]
\[ \Rightarrow \theta = \frac{5 \times 360°}{2r}\]
\[ \Rightarrow \theta = \frac{5 \times 360° }{2 \times 6}\]
\[ \Rightarrow \theta = 150° \]

Thus, the measure of the arc and length of the arc corresponding to the sector are 150º and 5 \[\pi\] cm, respectively.

  Is there an error in this question or solution?

APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 7: Mensuration
Practice set 7.4 | Q: 9 | Page no. 161
Solution The Area of a Sector of a Circle of 6 Cm Radius is 15 π Sq.Cm. Find the Measure of the Arc and Length of the Arc Corresponding to the Sector. Concept: Surface Area of a Combination of Solids.
S
View in app×