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Maths-

General

Easy

Question

A Sphere, cylinder and a cone are of the same radius and same height . Find the ratio of their curved surface areas and their volumes?

hint Hint:

Volume of sphere $equals 4 over 3 pi r cubed$
Volume of cylinder $r equals pi r squared h$

The correct answer is: 4:2:√2

Explanation:

We have given A Sphere, cylinder and a cone are of the same radius and same height.

We have to find the ratio of their curved surface areas and their volumes.

Step 1 of 1:
We have given a Sphere, cylinder and a cone are of the same radius and same height
Let that radius and height be r, h respectively.
Since, Sphere has equal radius and height.
So,
r = h
Then,
Volume of Sphere $equals 4 over 3 pi r cubed$
Volume of cylinder
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals pi r squared h end cell row cell equals pi r cubed end cell end table$
Volume of cone
$equals 1 third pi r squared h$
$equals 1 third pi r cubed$
Then Ratio of their volume will be
$equals 4 over 3 pi r cubed colon pi r cubed colon 1 third pi r cubed$
= 4:3:1
Step 2 of 2:
CSA of sphere
$equals 4 pi r squared$
CSA of cylinder
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 2 pi r h end cell row cell equals 2 pi r squared end cell end table$
CSA of cone
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals pi r open parentheses square root of r squared plus h squared end root close parentheses end cell row cell equals pi r open parentheses square root of r squared plus r squared end root close parentheses end cell row cell equals square root of 2 pi r squared end cell end table$
Then ratio of their CSA will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 4 pi r squared colon 2 pi r squared colon square root of 2 pi r squared end cell row cell equals 4 colon 2 colon square root of 2 end cell end table$

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