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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 1 · Set 1 · Q38
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)What is the total length of silver wire required ?What is the area of each sector of the brooch ?
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)
What is the total length of silver wire required ?
What is the area of each sector of the brooch ?
Marking-scheme solution
(i) \(\displaystyle r=\frac{35}{2} \mathrm{~cm}=17.5 \mathrm{~cm}\)
(ii) Circumference \(\displaystyle =2 \times \frac{22}{7} \times \frac{35}{2}=110 \mathrm{~cm}\)
(iii) (a) Total length of wire required \(\displaystyle =(5 \times 35+110) \mathrm{cm}\)
\[=285 \mathrm{~cm}
\]
(iii)
Central angle of each sector \(\displaystyle =\frac{360}{10}=36^{\circ}\) Area of each sector \(\displaystyle =\frac{36}{360} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} =\frac{385}{4}\) or \(\displaystyle 96.25 c m^{2}\)
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.