The minute hand of a clock is \(\sqrt{21}\) cm long. Find the area de

1.	The minute hand of a clock is \(\sqrt{21}\) cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.
Answer» Length of minute hand = \(\sqrt{21}\) cm Angle subtend by minute hand in 1 minute = \(\frac{360°}{60°}\) = 6° Angle subtend by minute hand in 5 minute (7-7.05) = 5 × 6 = 30° So, Area described by minute hand in 5 minute = \(\frac{θ}{360°}\timesπr^2\) = \(\frac{30}{360}\times\frac{22}7\times\sqrt{21}\times\sqrt{21}\) = \(\frac{1}{12}\times\frac{22}7\times21\) = 5.5 cm²

The minute hand of a clock is \(\sqrt{21}\) cm long. Find the area described by the minute hand on the face of the clock between 7.00 AM and 7.05 AM.

Answer»

Length of minute hand = \(\sqrt{21}\) cm

Angle subtend by minute hand in 1 minute = \(\frac{360°}{60°}\) = 6°

Angle subtend by minute hand in 5 minute (7-7.05) = 5 × 6 = 30°

So,

Area described by minute hand in 5 minute = \(\frac{θ}{360°}\timesπr^2\)

= \(\frac{30}{360}\times\frac{22}7\times\sqrt{21}\times\sqrt{21}\)

= \(\frac{1}{12}\times\frac{22}7\times21\)

= 5.5 cm²