SOLUTION: A lampshade in form of a frustum of a cone has the upper and lower diameters of 10cm and 20cm respectively and a height of 12cm. Calculate the area of the cloth required to cover t

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Question 975487: A lampshade in form of a frustum of a cone has the upper and lower diameters of 10cm and 20cm respectively and a height of 12cm. Calculate the area of the cloth required to cover the lampshade.
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Refer to your textbook or to this wikipedia article: https://en.wikipedia.org/wiki/Frustum .

If s is slant height, h is the frustrum height, and R and r are the bigger and smaller radii, then you can form a right triangle from the frustrum with the Pythagorean Theorem equation s%5E2=%28R-r%29%5E2%2Bh%5E2
and
Surface Area of the frustrum is pi%28R-r%29%2As.

The problem description gives you enough information for R and r, and you can find s.

s=sqrt%28%28R-r%29%5E2%2Bh%5E2%29
Surface Area is then highlight_green%28pi%28R-r%29%2Asqrt%28%28R-r%29%5E2%2Bh%5E2%29%29.
Radii are each half of the given diameters.

highlight%28SurfacArea=pi%2810%2B5%29sqrt%28%2810-5%29%5E2%2B12%5E2%29%29;
Compute the expression.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The lateral surface area of the frustum of a cone is given by:



Where and are the bottom and top radii.

Plug in your numbers and do the arithmetic. Don't forget that you are given the upper and lower diameters

John

My calculator said it, I believe it, that settles it