SOLUTION: Thank you very much for your help! The volume of a sphere is directly proportional to the cube of its diameter and is 288(pie)cm cubed when the diameter is 12 cm. Find the const

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Question 36029This question is from textbook Algebra II
: Thank you very much for your help!
The volume of a sphere is directly proportional to the cube of its diameter and is 288(pie)cm cubed when the diameter is 12 cm. Find the constant of proportionality in terms of (pie). Then write the formula for the volume of a sphere in terms of its diameter.
I know the answer is pie/6 and V=pie/6 d cubed. Thanks again! This question is from textbook Algebra II

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
hank you very much for your help!
The volume of a sphere is directly proportional to the cube of its diameter
THAT IS V=K*D^3..WHERE K IS A CONSTANT
and is 288(pie)cm cubed when the diameter is 12 cm.
HENCE
288*PI=K*12^3
K=288*PI/(12*12*12)=PI/6
Find the constant of proportionality in terms of (pie).
K=PI/6
Then write the formula for the volume of a sphere in terms of its diameter.
V=PI*D^3/6
I know the answer is pie/6 and V=pie/6 d cubed. Thanks again!
V I