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what is the formula for the volume of a sphere with diameter d?

 Mar 21, 2016

Best Answer 

 #3
avatar+25333 
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what is the formula for the volume of a sphere with diameter d?

 

r = Radius

d = diameter

 

\(\begin{array}{rcll} V &=& \dfrac43 \cdot \pi \cdot r^3 \quad & | \quad r = \dfrac{d}{2}\\\\ V &=& \dfrac43 \cdot \pi \cdot \left(\dfrac{d}{2} \right)^3 \\\\ V &=& \dfrac43 \cdot \pi \cdot \dfrac{d^3}{2^3} \\\\ V &=& \dfrac43 \cdot \pi \cdot \dfrac{d^3}{8} \\\\ V &=& \dfrac13 \cdot \pi \cdot \dfrac{d^3}{2} \\\\ V &=& \dfrac16 \cdot \pi \cdot d^3 \\\\ && \boxed{~ \begin{array}{rcll} V &=& \dfrac{\pi}{6} \cdot d^3 \end{array} ~} \end{array}\)

 

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 Mar 21, 2016
 #2
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Radius=Diameter/2

Volume of Sphere=4/3 x Pi x Radius^3

 Mar 21, 2016
 #3
avatar+25333 
+5
Best Answer

what is the formula for the volume of a sphere with diameter d?

 

r = Radius

d = diameter

 

\(\begin{array}{rcll} V &=& \dfrac43 \cdot \pi \cdot r^3 \quad & | \quad r = \dfrac{d}{2}\\\\ V &=& \dfrac43 \cdot \pi \cdot \left(\dfrac{d}{2} \right)^3 \\\\ V &=& \dfrac43 \cdot \pi \cdot \dfrac{d^3}{2^3} \\\\ V &=& \dfrac43 \cdot \pi \cdot \dfrac{d^3}{8} \\\\ V &=& \dfrac13 \cdot \pi \cdot \dfrac{d^3}{2} \\\\ V &=& \dfrac16 \cdot \pi \cdot d^3 \\\\ && \boxed{~ \begin{array}{rcll} V &=& \dfrac{\pi}{6} \cdot d^3 \end{array} ~} \end{array}\)

 

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heureka Mar 21, 2016

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