# The volume of a sphere is 5,572.45 in^3. To the nearest inch, what is the radius of the sphere?

The volume of a sphere is $$5,572.45 \in^3$$ To the nearest inch, what is the radius of the sphere?

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The volume of a sphere with radius rr is given by: $$\displaystyle{V}={\left(\frac{{4}}{{3}}\right)}π{r}^{{3}}$$
Substitute $$\displaystyle{V}={5572.45}\in^{{3}}$$ and solve for r: $$\displaystyle{5572.45}=\frac{{4}}{{3}}π{r}^{{3}}$$
Multiply both sides by $$\displaystyle\frac{{3}}{{4}}π$$: $$\displaystyle{5572.45}×\frac{{3}}{{4}}π={r}^{{3}}$$
Take the cube root:$$^3sqrt(5572.45\cdot(\frac{3}{4}(3.14)))=r r\sim11 \in$$.