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Maths-

General

Easy

Question

A Solid sphere and hemisphere have the same total surface areas. Find the ratio of their volumes ?

hint Hint:

Volume of a sphere $equals 4 over 3 pi r cubed$
Volume of a hemisphere $equals 2 over 3 pi r cubed$

The correct answer is: 1/√2

Explanation:

We have given a Solid sphere and hemisphere have the same total surface areas

We have to find the ratio of volumes of sphere and hemisphere

Step 1 of 1:
Let the radius of solid sphere be and hemisphere be r'
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 4 pi r squared equals 2 pi r to the power of straight prime 2 end exponent end cell row cell square root of 2 r equals r to the power of straight prime end cell end table$
Volume of sphere will be $V subscript s s end subscript equals 4 over 3 pi r cubed$
And volume of hemisphere will be
$V subscript h s end subscript equals 2 over 3 pi r to the power of straight prime 3 end exponent$
$equals 2 over 3 pi left parenthesis square root of 2 r right parenthesis cubed$
$equals square root of 2 4 over 3 pi r cubed$
Now Ratio of their volumes will be
$V subscript S S end subscript over V subscript h s end subscript equals fraction numerator 4 over 3 pi r cubed over denominator square root of 2 4 over 3 pi r cubed end fraction$
$V subscript s s end subscript over V subscript h s end subscript equals fraction numerator 1 over denominator square root of 2 end fraction$

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