Asked Jan 24, 2020

The line segment joining the origin to the point (h, r) is revolved about the x-axis to generate a cone of height h and base radius r. Find the cone’s surface area with the parametric equations x = ht, y = rt, 0<=t<= 1. Check your result with the geometry formula: Area = pai r(slant height)


Expert Answer

Step 1

Surface area formula of revolution about x axis is given by: 

Calculus homework question answer, step 1, image 1
Step 2

Given x=ht and y=rt and t is in [0,1] 

Use this information to find the surface area.

Calculus homework question answer, step 2, image 1
Step 3

To check the surface area geometrically , we draw the situation roughly.

OEF is right tr...

Calculus homework question answer, step 3, image 1

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