SOLUTION: To restore medieval castle in Eorope, the conical roof of one of its round towers had to be painted with a special protective silver paint. If the diameter of the conical roof base

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Question 80401: To restore medieval castle in Eorope, the conical roof of one of its round towers had to be painted with a special protective silver paint. If the diameter of the conical roof base 5.84 m and its altitude is 9.76 m, what is the cost of gilding the roof if the rate of painting the roof is equivalent to $27.50/m squared?
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST WE FIND THE SLOPE OF THE TOWER SURFACE USING THE TRIANGLE WITH SIDES OF 9.76 & 5.84/2=2.92 TO FIND THE SLOPE (HYPOTENUSE)
A^2+B^2=C^2
9.76^2+2.92^2=S^2
95.2576+8.5264=S^2
S^2=103.784
S=10.187 FOR THE SLOPE.
FORMULA FOR THE TOTAL SURFACE AREA OF A CONE IS
TSA=1/2piDS+piR^2 WHERE pi=3.14, D=DIAMETER, R=RADIUS
TSA=.5*3.14*5.84*10.187+3.14*2.92^2
TSA=93.4+26.77
TSA=120.17 IS THE TOTAL SURFACE AREA OF THE TOWER.
NOW WE MULTIPLY BY $27.50
120.17*27.50=$3,304.68 TO PAINT THE TOWER.