Q7 of 52 Page 154

In figure 7.32, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm. Find A (P-ABC).

Radius of circle, r = 3.4 cm


Perimeter of sector, P = 12.8


⇒ P = length of arc + 2× radius


⇒ Length of arc, l = P – 2×r


⇒ l = 12.8 – 2(3.4)


⇒ l = 6 cm


Let the ∠ APC be θ


As we know that,





Also ,



On Substituting the value of theta from above equation,





⇒ A = 10.2 sq. cm


∴ Area of Sector is 10.2 sq. cm


More from this chapter

All 52 →
5

Area of a sector of a circle of radius 15 cm is 30 cm2. Find the length of the arc of the sector.

 6

In the figure 7.31, radius of the circle is 7 cm and m(arc MBN) = 60°,find


(1) Area of circle


(2) A(O – MBN)


(3) A(O - MCN)

 8

In figure 7.33 O is the centre of the sector.∠ ROQ = ∠ MON = 60°. OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN.

9

In figure 7.34, if A(P-ABC) = 154 cm2radius of the circle is 14cm, find

(1) ∠ APC.


(2) l (arc ABC).