Question 239339
Each 5 minute segment is {{{1/12}}}  of a circle. In this problem the minute sweeps from 6:05 to 6:40. That is 7 five minute segments. Which means the area swept is 7/12 of the area on the clock face.

{{{AreaOfCircle = 2*pi*r^2}}}
You are told {{{r = 5cm}}}
{{{AreaOfCirlce = 2*pi*5^2}}}
{{{AreaOfCirlce = 50*pi}}}
But we only swept 7/12 of the full area. So the area we want is
{{{(7/12)*50pi}}}
{{{29.1667*pi}}}
{{{91.58}}}cm^2