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How do you find the volume of the sphere in terms of #pi# given #V=4/3pir^3# and d= 9 ft?

Answer 1

Sadie Adams

#243/2 pi#.

#V = 4/3 pi r^3#.

Given #d = 9#, then #r = d/2 = 9/2 #

#V = 4/3 pi (9/2)^3 = 243/2 pi#.

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Answer 2

Aurora Ayala

To find the volume of a sphere in terms of π given ( V = \frac{4}{3} πr^3 ) and the diameter ( d = 9 ) feet, first, you need to find the radius (( r )) using the formula for diameter (( d )):

( d = 2r )

Substitute the given diameter (( d = 9 ) feet) into the equation and solve for ( r ):

( 9 = 2r )

( r = \frac{9}{2} )

Now, substitute the value of ( r ) into the formula for volume (( V )):

( V = \frac{4}{3} π \left(\frac{9}{2}\right)^3 )

( V = \frac{4}{3} π \left(\frac{9}{2}\right) \left(\frac{9}{2}\right) \left(\frac{9}{2}\right) )

( V = \frac{4}{3} π \cdot \frac{729}{8} )

( V = \frac{243 π}{2} )

So, the volume of the sphere in terms of ( π ) is ( \frac{243 π}{2} ) cubic feet.

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Answer from HIX Tutor

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