$\"\"$

Consider the length of the pointer on voltmeter as radius.

Radius $\"\"$ cm.

The pointer rotation is the arc length of the circle.

Arc length $\"\"$ cm.

Arc length of the circle : $\"\"$ .

Where, $\"\"$ central angle.

$\"\"$

Substitute $\"\"$ cm and $\"\"$ cm in $\"\"$ .

$\"\"$ .

Divide each side by $\"\"$ .

$\"\"$

$\"\"$ radians.

$\"\"$

The central angle is $\"\"$ radians.