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:

Final Answer:

V =  189.1189

Step-by-step explanation:

$$\begin{gathered} a=4 \\ b=6 \\ \phi =50{}^{\circ } \\ b>a \\ r=a=4 \\ \tan \phi =r:h_1 \\ {h}_1=r/\tan \phi =r/\tan 50°=4/\tan 50°=4/1.191754=3.3564 \\ {h}_2=b-h_1=6-3.3564\doteq 2.6436 \\ S=\pi \cdot r^2=3.1416\cdot 4^2\doteq 50.2655 \\ {V}_1=\frac{1}{3}\cdot S\cdot h_1=\frac{1}{3}\cdot 50.2655\cdot 3.3564\doteq 56.237 \\ {V}_2=S\cdot h_2=50.2655\cdot 2.6436\doteq 132.8819 \\ V=V_1+V_2=56.237+132.8819=189.1189 \end{gathered}$$

Try another example