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A right circular cylinder just encloses a sphere of radius $ r $ (see in figure below). Find
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).
"
Given:
A right circular cylinder just encloses a sphere of radius \( r \).
To do:
We have to find
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).
Solution:
(i) Surface area of a sphere of radius $r = 4\pi r^2$
(ii) Height of cylinder $h =$ Diameter of the sphere
$=r+r$
$=2r$
Therefore,
The height of the cylinder is $2r$.
The radius of the cylinder $= r$
The curved surface area of the cylinder $= 2\pi rh$
$= 2\pi r(2r)$
$= 4\pi r^2$
(iii) Ratio of the surface area of the sphere to the curved surface area of the cylinder$=4\pi r^2:4\pi r^2$
$= 1:1$
The ratio of the areas obtained in (i) and (ii) is $1:1$.
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