Question

VODU

UNIPPO
1. Find the radius of a sphere with a volume (V) of 113 mm”.
O A.3 mm
O B.9 mm
O C. 16 mm
O D. 12 mm
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Answer 1

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=113 \end{cases}\implies 113=\cfrac{4\pi r^3}{3}\implies 339=4\pi r^3 \\\\\\ \cfrac{339}{4\pi }=r^3\implies 26.98\approx r^3\implies \sqrt[3]{26.98}=r\implies 2.999 \approx r\implies \stackrel{\textit{rounded up}}{3=r}`

Answer 2

r = ∛(3V/4π)

Explanation:

The formula for the volume of a sphere is V = (4/3)πr³.

We want to solve this first for r³ and then for r.

Multiplying both sides of V = (4/3)πr³ by 3 yields an equation without fractions: 3V = 4πr³.

Dividing both sides of this equation by 4π isolates r³:

3V

r³ = -------

4π

To find r, take the cube root of both sides of

3V

r³ = -------

4π

obtaining r = ∛(3V/4π)