Question

The formula for the volume of a sphere is y = 4/3 pi r^3 .
a. Solve the formula for r and write using positive rational exponents.
b. Find the radius, to the nearest hundredth, of a sphere with a volume of 15 in.3

Answer 1

You posted this question yesterday. Do you need more help?

Solve the formula for r and write using positive rational exponents.
can you solve for r^3 (get r^3 by itself on side of the = sign) ?

Answer 2

for info on using "rational exponents" (fancy word for a fraction used as an exponent)
see
http://www.khanacademy.org/math/arithmetic/exponents-radicals/world-of-exponents/v/zero--negative--and-fractional-exponents

Answer 3

so is this right for the first part of the problem? \[r = \sqrt[3]{\frac{ 3y }{ pi }}\]

Answer 4

almost, you left out the 4
\[r=\sqrt[3]{\frac{3y}{4 \pi} }\]

Answer 5

now use this idea
\[ \sqrt[n]{x} = x^{\frac{1}{n}}\]

Answer 6

im confused now

Answer 7

@phi

Answer 8

Did you look at the video?

Answer 9

y = 4/3 pi r^3
\[ y = \frac{4}{3} \pi r^3\]
In little steps:
multiply both sides by 3
\[ 3y = \cancel{3}\cdot \frac{4}{\cancel{3}} \pi r^3 \]
divide both sides by 4π
\[ \frac{3y}{4\pi} = \frac{\cancel{4\pi}}{\cancel{4\pi}} r^3\]
\[ r^3 = \frac{3y}{4\pi} \]
now raise both sides to the 1/3 power
\[ \left(r^3\right)^{\frac{1}{3}} = \left(\frac{3y}{4\pi}\right)^{\frac{1}{3}} \]

you should know (or watch more videos!) that
\[ (x^a)^b = x^{ab} \]
for this problem x is r, a is 3 and b is 1/3, and we can re-write the left side as
\[ r^{3\cdot \frac{1}{3}} = r^1= r\]
your answer is
\[ r= \left(\frac{3y}{4\pi}\right)^{\frac{1}{3}} \]

Answer 10

and then you plug in 15 for y right

Answer 11

yes, you can type into google
(45/(4*pi))^(1/3) =

or cube root (45/(4*pi)) =

Answer 12

thank you so much