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# 3d geo

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A cylinder with base of 3 units is inscribed in a sphere of radius 5 units. Find the total surface area of the cylinder plus the total surface area of the sphere.

Jan 9, 2021

#1
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can you send a sketch of the figure? to make the problem more understandable

Jan 9, 2021
#2
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Surface area of sphere   =   4pi * radius ^2 =  4 pi (5)^2  = 100pi

Look at the graph here  : https://www.desmos.com/calculator/e2lfbnrrza

We can imagine this graph as  being a  cross-sectional representation of our problem

The equation of the sphere's cross-section is  x^2 + y^2   = 25

Note  that    y =  sqrt  (25  -x^2)        (1)

Since  the base of the cylinder  =3, its radius  =1.5

Using (1), we can find (1/2)  of the  height of the cylinder as

y = sqrt ( 25  -1.5^2 )   = sqrt (  25 - 2.25) =  sqrt ( 100/4 - 9/4)  = sqrt (91) / sqrt (4)   =sqrt (91)  /2

So....the height is twice this  = sqrt (91)

So....the surface area of the sphere =   2pi radius * height  =  2pi (1.5)sqrt (91)   =  3pi sqrt (91)

Total surface area =    pi  ( 100 + 3sqrt (91)) ≈  404.07  units^2

Jan 9, 2021