Question

Type the correct answer in the box. assume π = 3.14. and round your answer to the nearest hundredth. 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 $ .

Answer 1

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,

$A_r=3\times4\\A_r=12\rm \;ft^2$

The radius of the semicircle is 1.5 m. The area of the semicircle is,

$A_{sc}=\dfrac{1}{2}\pi\times(1.5)^2\\A_{sc}=\dfrac{1}{2}(3.14)\times(1.5)^2\\A_{sc}=3.5325\rm\; ft^2$

The area of the composite figure is,

$A=12+3.5325\\A=15.5325\rm\;ft^2$

The rate of  painting is $2.00 per square foot. Thus the cost to paint the figure is,

$A=15.5325\times2\\A=31.065$

Hence, the cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

Learn more about the area  of composite figures here;

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