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

Bergen 2021-03-09 Answered

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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Expert Answer

Adnaan Franks
Answered 2021-03-10 Author has 7023 answers

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:\(^3sqrt(5572.45\cdot(\frac{3}{4}(3.14)))=r r\sim11 \in\).

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