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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Updated on: 10-Oct-2022

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