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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 1 · Set 1 · Q37
A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with…
A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs.
One such brooch is made with silver wire in the form of a circle with diameter $\displaystyle 35$ mm. The wire is also used in making $\displaystyle 5$ diameters which divide the circle into $\displaystyle 10$ equal sectors as shown in the figure. Based on the above given information, answer the following questions :
(i)
Find the central angle of each sector.
(ii)
Find the length of the arc ACB.
(iii)
(a)
Find the area of each sector of the brooch.
OR
(b)
Find the total length of the silver wire used.
Marking-scheme solution
(i) central angle \(\displaystyle =\frac{360^{0}}{10}=36^{\circ}\)
(ii) length of arc \(\displaystyle \mathrm{ACB}=\frac{1}{10} \times 2 \times \frac{22}{7} \times \frac{35}{2}=11 \mathrm{~mm}\)
(iii) (a) Area of each sector of the brooch \(\displaystyle =\frac{1}{10} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2}\)
\[=\frac{385}{4} \mathrm{~mm}^{2} \text { or } 96.25 \mathrm{~mm}^{2}
\]
(iii) (b) length of silver wire used \(\displaystyle =2 \times \frac{22}{7} \times \frac{35}{2}+5 \times 35\)
\[\text { = } 285 \text { mm }
\]
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.