Question

The length of minute hand of a clock is 5cm.Find the the area swept by the minute hand during the time period 6:05 amd and 6:40.​

Answer 1

Given :-

The length of a minute hand of a clock is 5cm

To Find :-

The area swept by the Minute hand of the clock between the time period 6 : 05 and 6 : 40

Solution :-

At First see , the attachment from their you can clearly see that angle made by the minute hand from 6 : 05 to 6 : 40 is 210°

Now , It is not a minor sector but the part from 6 : 40 to 6 : 05 is a minor Sector . So , we will simply Find the area of the clock and then subtract the area of ACBX from the clock.

Here ,

• Radius of clock = 5 cm

Now , Area of clock :-

$\quad \qquad { \tt{ Area_{(Clock)} = πr² } }$

$\quad \qquad { : \longmapsto \tt { Area_{(Clock)} = \dfrac{22}{7} × 5 × 5 } }$

$\quad \qquad { : \longmapsto \tt { Area_{(Clock)} = \dfrac{550}{7} cm² } }$

Now , Angle made by The Part ACBX is 360° - 210° = 150°

Now ;

$\quad \qquad { \tt{ Area_{(ACBX)} = \dfrac{πr² \theta}{360°} } }$

$\quad \qquad { \tt : \longmapsto { Area_{(ACBX)} = \dfrac{22 × 5 × 5 × 150}{7 × 360} } }$

$\quad \qquad { \tt { : \longmapsto Area_{(ACBX)} = \dfrac{550 × 5}{7 × 12} cm² } }$

Now ;

$\quad \qquad { \tt { Area_{( Required )} = Area_{(Clock)} - Area_{(ACBX)} } }$

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{550}{7} - \dfrac{550 × 5 }{7 × 12} cm² } }$

Take 550/7 as common ;

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{550}{7} × { \bigg [ 1 - \dfrac{5}{12} } \bigg ] } }$

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{550}{7} × { \bigg [ \dfrac{12 - 5}{12} } \bigg ] } }$

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{550}{7} × { \bigg [ \dfrac{7}{12} } \bigg ] } }$

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{550}{7} × \dfrac{7}{12} } }$

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{550}{12} } }$

$\quad \qquad { \tt : \longmapsto { Area_{( Required )} = \dfrac{275}{6} cm² } }$

Henceforth , The Required Answer is 275/6 cm²

Answer 2

Step-by-step explanation:

The time gap is 35 minutes.

In 60 minutes minute hand moves through 360 degrees.

In 35 minutes minute hand moves through 360/60 * 35 = 210.

The area swept = 210/360 * pi *r*r

= 210/360* 22/7 * 5 * 5

= 275/6

= 45.8.

376

4.0

69

Hope this helps!