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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 1 · Set 2 · Q37
A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the…
A brooch is crafted from silver wire in the shape of a circle with a diameter of $\displaystyle 35$ cm . The wire is also used to create $\displaystyle 5$ diameters, dividing the circle into $\displaystyle 10$ equal sectors as shown in figure.
Based on the above information, answer the following questions :
(i)
What is the radius of circle ?
(ii)
What is the circumference of the brooch ?
(iii)
(a)
What is the total length of silver wire required ?
OR
(b)
What is the area of each sector of the brooch ?
Marking-scheme solution
(i) \(\displaystyle r=\frac{35}{2} \mathrm{~cm}=17.5 \mathrm{~cm}\)
I
(ii) Circumference \(\displaystyle =2 \times \frac{22}{7} \times \frac{35}{2}=110 \mathrm{~cm}\)
I
(iii) (a) Total length of wire required \(\displaystyle =(5 \times 35+110) \mathrm{cm}\)
\[=285 \mathrm{~cm}
\]
I
II
II
(iii) (b) Central angle of each sector \(\displaystyle =\frac{360}{10}=36^{\circ}\)
\[\begin{aligned}
\text { Area of each sector } & =\frac{36}{360} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \\
& =\frac{385}{4} \text { or } 96.25 \mathrm{~cm}^{2}
\end{aligned}
\]
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