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Question
In the above figure, a sphere is placed in a cylinder. It touches the top, bottom and curved surface of the cylinder. If the radius of the base of the cylinder is ‘r’, write the answer to the following questions.
a. What is the height of the cylinder in terms of ‘r’?
b. What is the ratio of the curved surface area of the cylinder and the surface area of the sphere?
c. What is the ratio of volumes of the cylinder and of the sphere?
Solution
(a)
Vol. = `pir^2h`
h = `1/(pir^2)`
(b)
`"CSA of Cylinder"/"SA of sphere"`
= `(2pirh + 2pir^2)/(4pir^2)`
=`(2pir(h + r))/(2pir (2r))`
= `(h + r)/(2r)`
(c)
`"Vol. of cylinder"/"Vol. of a sphere"`
= `(pir^2h)/(4/3pir^3)`
= `(pir^2(h))/(pir^2(4/3r)) = h/r xx 3/4`
= `(3h)/(4r)`
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