In $\odot(O, 4)$,$\widehat{ACB}$ is a minor arc and $m \angle AOB = 45^\circ$. Then,the length of minor $\widehat{ACB}$ is $\ldots \ldots \ldots \ldots$

$A$ brooch is made with silver wire in the form of a circle with diameter $35 \, mm$. The wire is also used in making $5$ diameters which divide the circle into $10$ equal sectors as shown in the figure. Find:
$(i)$ The total length of the silver wire required.
$(ii)$ The area of each sector of the brooch. [Use $\pi = \frac{22}{7}$]

In a circle with radius $8.4 \, cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to this arc.

The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

$A$ round table cover has six equal designs as shown in the figure. If the radius of the cover is $28\, cm$,find the cost of making the designs at the rate of $Rs.\, 0.35$ per $cm^2$. (in $Rs.$) (Use $\sqrt{3}=1.7$)

The maximum area of a triangle inscribed in a semicircle having radius $10 \, cm$ is $\ldots \ldots \ldots \, cm^2$.