The region in the first quadrant bounded by the line `3x+2y =7` and the coordinate axes is rotated about the x-axis .What is the volume of the resulting solid ?

Options

A. 8 units`""^(3)`
B. 20 units`""^(3)`
C. 30 units`""^(3)`
D. 40 units`""^(3)`

Answer

C

Explanation

The line `3x + 2y =7 ` has x - intercept ` (7)/(3)` and y -intercept `(7)/(2)` The part of this line that lies in the first quadrant forms a triangle with the coordinate axes .Rotating this
Triangle about the x-axis produces a cone with radius `(7)/(2)` and height `(7)/(3)` The volume of this cone is `(1)/(3) pi ((7)/(2))^(2)((7)/(3))~~30`