Answer :
The cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.
How to find the area of the composite figures?
To find area of the composite figures,
- Separate the figure.
- Calculate the are of the each figure by which the composite figure is made of.
- Add the area of all the individual figures to get the total area of composite figures.
The dimentions of the rectangle is 3 by 4 foot. The area of the rectangle is,
[tex]A_r=3\times4\\A_r=12\rm \;ft^2[/tex]
The radius of the semicircle is 1.5 m. The area of the semicircle is,
[tex]A_{sc}=\dfrac{1}{2}\pi\times(1.5)^2\\A_{sc}=\dfrac{1}{2}(3.14)\times(1.5)^2\\A_{sc}=3.5325\rm\; ft^2[/tex]
The area of the composite figure is,
[tex]A=12+3.5325\\A=15.5325\rm\;ft^2\\[/tex]
The rate of painting is $2.00 per square foot. Thus the cost to paint the figure is,
[tex]A=15.5325\times2\\A=31.065[/tex]
Hence, the cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.
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