A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sector as shown in figure. Find :
(i) The total length of the silver wire required.

(ii) The area of each sector of the brooch.



Answer :


(i) Length of silver wire used to make a brooch

\( = \ 2 \pi r \), where \( r \ = \ \frac{35}{2} \)mm

\( = \ 2 \ × \ \frac{22}{7} \ × \ \frac{35}{2} \ = \ 110 \) mm

Wire used in 5 diameters \( = 5 \ × \ 35 \ = \ 175 \) mm

\(\therefore \) Total wire used \(= (110 \ + \ 175) \ = \ 285 \) mm

(ii) The area of each sector of the brooch

\( = \ \frac{1}{10} \ × \) Area of the circle

\( = \ \frac{1}{10} \ × \ \pi r^2 \), where \(r \ = \ \frac{35}{2} \)mm

\(= \ \frac{1}{10} \ × \ \frac{22}{7} \ × \ ( \frac{35}{2} )^2 \ = \ \frac{385}{4} \) mm2

NCERT solutions of related questions for Areas related to circles

NCERT solutions of related chapters class 10 maths

NCERT solutions of related chapters class 10 science