Right-angled trapezoid

A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is:

Correct answer:

V =  189.1189

Step-by-step explanation:

a=4 b=6 φ=50   b>a  r=a=4 tan φ = r : h1  h1=r/tanφ=r/tan50° =4/tan50° =4/1.191754=3.3564 h2=bh1=63.35642.6436  S=π r2=3.1416 4250.2655 V1=31 S h1=31 50.2655 3.356456.237 V2=S h2=50.2655 2.6436132.8819  V=V1+V2=56.237+132.8819=189.1189

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