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Sphere
A sphere is cutted and a new sphere is made from it.The new sphere's curved surface is half of the first sphere .Then what is the ratio of the cutted portion's volume and the remaining portion's volume?
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****** of * sphere = ********************* * * ******* area ** * ****** = ********************* Let *** volume *** surface **** ** ******** **** ******* and new ****** ** ** ** *** ** & ** ************ And let r1 *** ** be *** respective radii ** *** *********** *** ****** ***** *** * 2 * ***** ** ******* **** a1= a2 * * ⇒4 ** ******************* * * π r2^2 * * (Dividing both *** & RHS *** π *********************** * r2^2 * 2 or ** * ** ***** *** ** = ** X√2Now ** **** ** find v2/(v1-v2) ( ****** ********* ******* ****** * ***** )∴v2=4πr2^3 * 3 ***** v1=4πr1^3 / *** ***** ******** ******************** / * *** v2 * ******* * *********************** * * ) ** * 4π(r1- ******************** * * ) = ******************* * (r1- ******************** * ***** 4π /3 cancels *** **** **** numerator and denominator * *** ** * (v1-v2)= r2^3 * **** ******************** = **** * **** ************************** / ( ** ***** * ** *********************************** =((r2/r2(√2 * 1 ))^3 * * /(√2 * * ****************** * ** / ***** * 1 ))^3 *** *** ** multiply **** *** ********* *** *********** ** ((√2 + * * ** we haveratio ** *** ************ volume and *** ********* ********* ****** *** * ***** * * ******************* * ******* + * ) * ****** + * * ****** * * ******************** * ******* + 1 * / ************************ * 1^2))) ***************** ********* * ***** * ******************* ************************** * * * X(√2 * * ************************ * ******************** * ** * ******* + * ) * ************************** + * ************************ )^3+ 1^3 * * ****** * ***** * ** * 2√2+ 1 * 3 *********** 3 ****** ******* * 3 * * + 3√2= * * ********** *** ratio ** *** ************ ****** and *** ********* ********* ****** ** * *****
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*** ****** ** cutted ****** is ******** ** ***** ** *** first Then *** ******* are expressed and *** ********** worked *** ** obtain the ****** of ********* *********** ***** *** ***** is ******** ** dividing *** *********** the ******* ** *********** ******** **** for **** ************
