How to find the radius of a sphere - High School Math

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Question

Find the radius of a sphere whose surface area is $SA=100cm^{2}$ .

Answer

We know that the surface area of the spere is $SA=100cm^{2}$ .

$SA=4\pi r^{2}$

$100cm^{2}=4\pi r^{2}$

Rearrange and solve for .

$r^{2}=\frac{100cm^{2}}{4\pi}$

$\dpi{100} r=\sqrt{\frac{100cm^{2}}{4\pi}}$

$\dpi{100}\rightarrow 2.82cm$

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Question

What is the radius of a sphere that has a surface area of $16\pi$ ?

Answer

The standard equation to find the area of a sphere is $SA=4\pi r^2$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt{\frac{SA}{4\pi }}$

To find the answer, substitute the given surface area into this equation and solve for the radius:

$r=\sqrt{\frac{16\pi }{4\pi }}=\sqrt{4}=2$

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Question

Given that the volume of a sphere is $12\pi$ , what is the radius?

Answer

The standard equation to find the volume of a sphere is

$V=\frac{4}{3}\pi r^3$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt[3]{\frac{3V}{4\pi }}$

Substitute the given volume into this equation and solve for the radius:

$r=\sqrt[3]{\frac{3V}{4\pi }}=\sqrt[3]{\frac{3\cdot 12\pi }{4\pi }}=\sqrt[3]{\frac{36\pi }{4\pi }}=\sqrt[3]{9 }$

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Question

What is the radius of a sphere with a volume of $288\pi$ ?

Answer

$V=\frac{4}{3}\pi r^3$

$288\pi=\frac{4}{3}\pi r^3$

$\frac{288\pi}{\pi}=\frac{4\pi r^3}{3\pi}$

$288=\frac{4r^3}{3}$

$(288)(\frac{3}{4})=\frac{3}{4}(\frac{4r^3}{3})$

$\sqrt[3]{216}=\sqrt[3]{r^3}$

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