Question 1001532


At the rate of $2.00 per square foot, the cost of painting the rectangular board with a semicircular top shown in the figure is $?

first find the area of the given figure:

it consists of a rectangle, dimensions {{{L =4ft}}} and {{{W =3ft}}}=>{{{A[r]=4ft*3ft=12ft^2}}}
then, you have one half of the area of the circle that has diameter {{{R=3ft}}}=> radius will be {{{r=1.5ft}}}: the area of that half will be {{{A[c]=(r^2*pi)/2=((1.5ft)^2*3.14)/2=(2.25ft^2*3.14)/2=7.065ft^2/2 =3.5325ft^2}}}

the area of the given figure: 

{{{A=A[r]+A[c]}}}

{{{A=12ft^2+3.5325ft^2}}}

{{{A=15.5325ft^2}}}

At the rate of ${{{2.00 }}}per square foot, the cost will be:

${{{15.5325*2=31.07}}}