If the area of a sphere is $frac81pisqrt27$ what is it's radius? [closed]

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I've been stuck in this textbook problem for so long now, basically if the radius is $R$ then:



$4pi R^2 = frac81pisqrt27$



The textbook says the solution is one of these:



$a) frac32sqrt3$



$b) frac32sqrt[4]3$



$c) frac92$



$d) frac94sqrt3$



The solution is suppose to be $b)$ but I have never been able to get that answer.




algebra-precalculus




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closed as off-topic by Andrés E. Caicedo, amWhy, Xander Henderson, Taroccoesbrocco, Leucippus Aug 10 at 4:30


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Also, welcome to Math.SE! If you can let us know what answers you've gotten, and how you've gotten them, we'll be better able (and more likely) to help you.
    – Cameron Buie
    Aug 9 at 23:39














up vote
-1
down vote

favorite












I've been stuck in this textbook problem for so long now, basically if the radius is $R$ then:



$4pi R^2 = frac81pisqrt27$



The textbook says the solution is one of these:



$a) frac32sqrt3$



$b) frac32sqrt[4]3$



$c) frac92$



$d) frac94sqrt3$



The solution is suppose to be $b)$ but I have never been able to get that answer.




algebra-precalculus




share|cite|improve this question














closed as off-topic by Andrés E. Caicedo, amWhy, Xander Henderson, Taroccoesbrocco, Leucippus Aug 10 at 4:30


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Also, welcome to Math.SE! If you can let us know what answers you've gotten, and how you've gotten them, we'll be better able (and more likely) to help you.
    – Cameron Buie
    Aug 9 at 23:39












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











I've been stuck in this textbook problem for so long now, basically if the radius is $R$ then:



$4pi R^2 = frac81pisqrt27$



The textbook says the solution is one of these:



$a) frac32sqrt3$



$b) frac32sqrt[4]3$



$c) frac92$



$d) frac94sqrt3$



The solution is suppose to be $b)$ but I have never been able to get that answer.




algebra-precalculus




share|cite|improve this question














I've been stuck in this textbook problem for so long now, basically if the radius is $R$ then:



$4pi R^2 = frac81pisqrt27$



The textbook says the solution is one of these:



$a) frac32sqrt3$



$b) frac32sqrt[4]3$



$c) frac92$



$d) frac94sqrt3$



The solution is suppose to be $b)$ but I have never been able to get that answer.





algebra-precalculus





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 11 at 13:12









Chris Custer

5,5862622




5,5862622










asked Aug 9 at 23:30









Richard Paul Astley

62




62




closed as off-topic by Andrés E. Caicedo, amWhy, Xander Henderson, Taroccoesbrocco, Leucippus Aug 10 at 4:30


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Andrés E. Caicedo, amWhy, Xander Henderson, Taroccoesbrocco, Leucippus Aug 10 at 4:30


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, Taroccoesbrocco, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Also, welcome to Math.SE! If you can let us know what answers you've gotten, and how you've gotten them, we'll be better able (and more likely) to help you.
    – Cameron Buie
    Aug 9 at 23:39
















  • Also, welcome to Math.SE! If you can let us know what answers you've gotten, and how you've gotten them, we'll be better able (and more likely) to help you.
    – Cameron Buie
    Aug 9 at 23:39















Also, welcome to Math.SE! If you can let us know what answers you've gotten, and how you've gotten them, we'll be better able (and more likely) to help you.
– Cameron Buie
Aug 9 at 23:39




Also, welcome to Math.SE! If you can let us know what answers you've gotten, and how you've gotten them, we'll be better able (and more likely) to help you.
– Cameron Buie
Aug 9 at 23:39










2 Answers
2






active

oldest

votes

















up vote
3
down vote



accepted










From $4pi R^2 = frac81pisqrt27$ divide by $4pi$ to get
$$R^2=frac814sqrt27=frac3^42^2cdot 3^frac32=frac3^frac524
$$
Then square root to get
$$R=frac3^frac542=frac3^1+frac142=frac323^frac14=frac32sqrt[4]3
$$



as required!






share|cite|improve this answer




















  • Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
    – Richard Paul Astley
    Aug 10 at 0:06











  • No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
    – Malkin
    Aug 10 at 0:15

















up vote
-1
down vote













$$4pi R^2=frac 81pisqrt27implies R^2=frac814sqrt27implies R=frac92sqrt[4]27implies R=frac3^22cdot 3^frac34implies R=frac 3^frac542implies R=frac32cdot sqrt[4]3$$.






share|cite|improve this answer





























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    3
    down vote



    accepted










    From $4pi R^2 = frac81pisqrt27$ divide by $4pi$ to get
    $$R^2=frac814sqrt27=frac3^42^2cdot 3^frac32=frac3^frac524
    $$
    Then square root to get
    $$R=frac3^frac542=frac3^1+frac142=frac323^frac14=frac32sqrt[4]3
    $$



    as required!






    share|cite|improve this answer




















    • Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
      – Richard Paul Astley
      Aug 10 at 0:06











    • No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
      – Malkin
      Aug 10 at 0:15














    up vote
    3
    down vote



    accepted










    From $4pi R^2 = frac81pisqrt27$ divide by $4pi$ to get
    $$R^2=frac814sqrt27=frac3^42^2cdot 3^frac32=frac3^frac524
    $$
    Then square root to get
    $$R=frac3^frac542=frac3^1+frac142=frac323^frac14=frac32sqrt[4]3
    $$



    as required!






    share|cite|improve this answer




















    • Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
      – Richard Paul Astley
      Aug 10 at 0:06











    • No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
      – Malkin
      Aug 10 at 0:15












    up vote
    3
    down vote



    accepted







    up vote
    3
    down vote



    accepted






    From $4pi R^2 = frac81pisqrt27$ divide by $4pi$ to get
    $$R^2=frac814sqrt27=frac3^42^2cdot 3^frac32=frac3^frac524
    $$
    Then square root to get
    $$R=frac3^frac542=frac3^1+frac142=frac323^frac14=frac32sqrt[4]3
    $$



    as required!






    share|cite|improve this answer












    From $4pi R^2 = frac81pisqrt27$ divide by $4pi$ to get
    $$R^2=frac814sqrt27=frac3^42^2cdot 3^frac32=frac3^frac524
    $$
    Then square root to get
    $$R=frac3^frac542=frac3^1+frac142=frac323^frac14=frac32sqrt[4]3
    $$



    as required!







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Aug 9 at 23:53









    Malkin

    1,482523




    1,482523











    • Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
      – Richard Paul Astley
      Aug 10 at 0:06











    • No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
      – Malkin
      Aug 10 at 0:15
















    • Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
      – Richard Paul Astley
      Aug 10 at 0:06











    • No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
      – Malkin
      Aug 10 at 0:15















    Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
    – Richard Paul Astley
    Aug 10 at 0:06





    Thank you, but how did you get from $frac3^42^2⋅3^frac32$ to $frac3^frac524$?
    – Richard Paul Astley
    Aug 10 at 0:06













    No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
    – Malkin
    Aug 10 at 0:15




    No problem. In that expression, the $2^2$ becomes the $4$ and $frac3^43^frac32=3^4-frac32=3^frac52$.
    – Malkin
    Aug 10 at 0:15










    up vote
    -1
    down vote













    $$4pi R^2=frac 81pisqrt27implies R^2=frac814sqrt27implies R=frac92sqrt[4]27implies R=frac3^22cdot 3^frac34implies R=frac 3^frac542implies R=frac32cdot sqrt[4]3$$.






    share|cite|improve this answer


























      up vote
      -1
      down vote













      $$4pi R^2=frac 81pisqrt27implies R^2=frac814sqrt27implies R=frac92sqrt[4]27implies R=frac3^22cdot 3^frac34implies R=frac 3^frac542implies R=frac32cdot sqrt[4]3$$.






      share|cite|improve this answer
























        up vote
        -1
        down vote










        up vote
        -1
        down vote









        $$4pi R^2=frac 81pisqrt27implies R^2=frac814sqrt27implies R=frac92sqrt[4]27implies R=frac3^22cdot 3^frac34implies R=frac 3^frac542implies R=frac32cdot sqrt[4]3$$.






        share|cite|improve this answer














        $$4pi R^2=frac 81pisqrt27implies R^2=frac814sqrt27implies R=frac92sqrt[4]27implies R=frac3^22cdot 3^frac34implies R=frac 3^frac542implies R=frac32cdot sqrt[4]3$$.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Aug 11 at 12:50

























        answered Aug 9 at 23:57









        Chris Custer

        5,5862622




        5,5862622












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