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.
+59 can you send a sketch of the figure? to make the problem more understandable
+130071 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
