Homework SourseFind the lateral surface area of the cone generated by revol
Find the lateral surface area of the cone generated by revolving the line segment y = x/2, 0<= x <= 4, about the y-axis.
Check your answer with the geometry formula.
lateral surface area = 1/2 * base circumference * slant height
Check your answer with the geometry formula.
lateral surface area = 1/2 * base circumference * slant height
Solution
When x = 0, y = 0 and when x = 10, y =2 Since y = x/5, x = 5*y The circumference of a circle is p*d = 2*p*r and in this case r = x However we are integrating relative to the change in y, so we will use the linear equation x = 5*y and the circumference is: 2*p*5*y ?y as ?y-->0 = 2*p*5*y dy 2 ? 10*p*y dy 0 .........................2 = 10*p*((y^2)/2) ] .........................0 = 10*p*(4/2) = 20*p = 20*3.1416 = 62.832
