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# volume of sphere formula with d

0
861
3
+371

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

Mar 21, 2016

#3
+25333
+5

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

d = diameter

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

Mar 21, 2016

#2
0

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

Mar 21, 2016
#3
+25333
+5

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

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