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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 4 · Set 1 · Q22
(a) The minute hand of a clock is 14 cm long. Find the area on the face of the clock described by the minute hand in 5 minutes.
(a)
The minute hand of a clock is $\displaystyle 14$ cm long. Find the area on the face of the clock described by the minute hand in $\displaystyle 5$ minutes.
OR
(b)
Find the length of the arc of a circle which subtends an angle of $\displaystyle 60$° at the centre of the circle of radius $\displaystyle 42$ cm .
Marking-scheme solution
(a)
Angle subtended in $\displaystyle 5$ min. = $\displaystyle 30$°
Area described by minute hand \(\displaystyle =\frac{30}{360} \times \frac{22}{7} \times 14 \times 14\)
\[=\frac{154}{3} \mathrm{~cm}^{2} \text { or } 51.33 \mathrm{~cm}^{2} \text { approx. }
\]
OR
(b)
\[\begin{aligned}
\text { Length of arc } & =2 \times \frac{22}{7} \times 42 \times \frac{60}{360} \\
& =44 \mathrm{~cm}
\end{aligned}
\]
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