Question

Find the lateral​ (side) surface area of the cone generated by revolving the line segment y equals nine sevenths x ​, 0 less than or equals x less than or equals 7​, about the​ x-axis. Check your answer with the following geometry formula. Lateral surface areaequalsone half times base circumference times slant height

Answer 1

Answer:

lateral​ surface area  =118.42

Step-by-step explanation:

y= 9x/7

dx/dy =

Given x range as  from 0 ≤ x ≤ 7 ⇒ The range of x is

a= 9x/7 = 9(0)/4 = 0

b = 9x/7= 9(7)/4 = 9

lateral​ surface area of the cone

$\int\limits^b_a {2\pi x\sqrt{1 + (\frac{dx}{dy} })^2 } \, dx \\\\\int\limits^9_0 {2\pi (\frac{9x}{7} )\sqrt{1 + (\frac{9}{7} })^2 } \, dx$

=$\frac{18\pi \sqrt{130} }{49} \int\limits^9_0 {x} \, dx$

=118.42