The length of the minute hand of a clock is 5 | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

We know that, in $60$ min, minute hand revolving $=360^{\circ}$

In $1$ min, minute hand revolving $=\frac{360^{\circ}}{60^{\circ}}$

$	herefore$

Vedclass · Accepted Answer

$45 \frac{5}{6}$

Vedclass · Answer

We know that, in $60$ min, minute hand revolving $=360^{\circ}$

In $1$ min, minute hand revolving $=\frac{360^{\circ}}{60^{\circ}}$

$	herefore$ In ($6.05$ am to $6: 40 am )=35 min$

minute hand revolving $=\frac{360^{\circ}}{60^{\circ}} 	imes 35=6 	imes 35$

Given that, length of minute hand $(r)=5\, cm$.

$	herefore$ Area of sector AOBA with angle $\angle O=\frac{\pi r^{2}}{360} 	imes \angle O$

$=\frac{22}{7} \frac{(5)^{2}}{360^{\circ}} 	imes 6 	imes 35$

$=\frac{22}{7} 	imes \frac{5 	imes 5}{360^{\circ}} 	imes 6 	imes 35$

$=\frac{22 	imes 5 	imes 5 	imes 5}{60^{\circ}}=\frac{22 	imes 5 	imes 5}{12}$

$=\frac{11 	imes 5 	imes 5}{6}=\frac{275}{6}=45 \frac{5}{6} cm ^{2}$

Hence, the required area swept by the minute land is $45 \frac{5}{6} \,cm ^{2}$.

The length of the minute hand of a clock is $5\, cm$. Find the area swept by the minute hand during the time period $6: 05$ $a.m.$ and $6: 40$ $a.m.$ (in $cm^2$)

Similar Questions

As shown in the diagram, the length of square $A B C D$ is $21\, cm .$ $\widehat{ A P C }$ is an arc of $\odot(B, BA )$ and $\widehat{A Q C}$ is an arc of $\odot( D , DA ) .$ Find the area of the shaded (ruled) portion. (in $cm^2$)

The length of the minute hand of a clock is $7\,cm$. The area of the region swept by it in $20$ minutes is $\ldots \ldots \ldots . cm ^{2}$.

In a circle with radius $42\, cm$, a minor arc subtends an angle of measure $60$ at the centre. Find the area of the minor sector and the minor segment corresponding to this arc. $(\sqrt{3}=1.73)$

In $\odot( O , 12)$, minor $\widehat{ ACB }$ subtends an angle of measure $30$ at the centre. Then. the length of major $\widehat{A D B}$ is $\ldots \ldots \ldots . . cm .$

In a circle with radius $6\, cm ,$ a minor are subtends an angle of measure $60$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.