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

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Question

What is the diameter of a sphere with a volume of $36\pi$ ?

Answer

To find the diameter of a sphere we must use the equation for the volume of a sphere to find the radius which is half of the diameter.

The equation is

First we enter the volume into the equation yielding $36\pi=(\frac{4}{3})(\pi)(r^{3})$

We then divide each side by to get $36=(\frac{4}{3})(r^{3})$

We then multiply each side by to get $27=r^{3}$

We then take the cubic root of each side to solve for the radius $\sqrt[3]{27}=\sqrt[3]{r^{3}}$

The radius is

We then multiply the radius by 2 to find the diameter

The answer for the diameter is .

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Question

If the surface area of a sphere is $64\pi$ , find the diameter of this sphere.

Answer

The standard equation to find the surface area of a sphere is

$SA=4\pi r^2$ where denotes the radius. Rearrange this equation in terms of :

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

Substitute the given surface area into this equation and solve for the radius and then double the radius to get the diameter:

$r=\sqrt{\frac{64\Pi }{4\Pi }}=\sqrt{16}=4$

$diameter=2\cdot r=2\cdot 4=8$

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Question

Given that the volume of a sphere is $4\pi$ , find the diameter.

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. Double the radius to find the diameter:

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

$diameter=2\cdot r=2\sqrt[3]{3}$

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Question

The volume of a sphere is $2 8 8 \pi$ . What is the diameter?

Answer

To find the diameter of the sphere, we need to find the radius.

The volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our given values.

$2 88\pi=\frac{4}{3}\pi r^3$

Notice that the $\pi$ 's cancel out.

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

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

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

The diameter is twice the radius, so .

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Question

What is the diameter of a sphere with a volume of $36\pi$ ?

Answer

The volume of a sphere is determined by the following equation:

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

$36\pi=\frac{4}{3}\pi r^3$

$(\frac{3}{4})36\pi=(\frac{3}{4})(\frac{4}{3})\pi r^3$

$\frac{27\pi}{\pi}=\frac{\pi r^3}{\pi}$

$\sqrt[3]{27}=\sqrt[3]{r^3}$

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