How to find the radius of a sphere - GRE Quantitative Reasoning

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Question

What is the radius of a sphere with volume $36\pi$ cubed units?

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Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

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Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

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Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

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Question

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

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Answer

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

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Question

What is the radius of a sphere with volume $36\pi$ cubed units?

Tap to reveal answer

Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

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Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

Tap to reveal answer

Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

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Question

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

Tap to reveal answer

Answer

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

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Question

What is the radius of a sphere with volume $36\pi$ cubed units?

Tap to reveal answer

Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

← Didn't Know|Knew It →

Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

Tap to reveal answer

Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

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Question

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

Tap to reveal answer

Answer

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

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Question

What is the radius of a sphere with volume $36\pi$ cubed units?

Tap to reveal answer

Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

← Didn't Know|Knew It →

Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

Tap to reveal answer

Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

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Question

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

Tap to reveal answer

Answer

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

← Didn't Know|Knew It →

Question

What is the radius of a sphere with volume $36\pi$ cubed units?

Tap to reveal answer

Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

← Didn't Know|Knew It →

Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

Tap to reveal answer

Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

← Didn't Know|Knew It →

Question

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

Tap to reveal answer

Answer

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

← Didn't Know|Knew It →

Question

What is the radius of a sphere with volume $36\pi$ cubed units?

Tap to reveal answer

Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

← Didn't Know|Knew It →

Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

Tap to reveal answer

Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

← Didn't Know|Knew It →

Question

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

Tap to reveal answer

Answer

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

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

And thus the volume of the largest possible sphere to fit into this prism is

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

← Didn't Know|Knew It →

Question

What is the radius of a sphere with volume $36\pi$ cubed units?

Tap to reveal answer

Answer

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

← Didn't Know|Knew It →

Question

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

Tap to reveal answer

Answer

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

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How to find the radius of a sphere - GRE Quantitative Reasoning

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume cubed units?

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r: Therefore, the radius of the sphere is 3.

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

The formula for the volume of a sphere is where is the radius of the sphere. Therefore, , giving us .

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .

A rectangular prism has the dimensions $9\textup{ x }6\textup{ x }12$ . What is the volume of the largest possible sphere that could fit within this solid?

What is the radius of a sphere with volume $36\pi$ cubed units?

The volume of a sphere is represented by the equation $\frac{4}{3}$\pi $r^3$ . Set this equation equal to the volume given and solve for r:

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

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

$27\pi=\pi $r^3$$

Therefore, the radius of the sphere is 3.

The formula for the volume of a sphere is

$v=\frac{4}{3}$(\pi $r^3$)$ where is the radius of the sphere.

Therefore,

$r=\sqrt[3]{$\frac{3v}{(4\pi)}$}$

$r=\sqrt[3]{$\frac{3(268.08)}{(4\pi)}$}=\sqrt[3]{63.999}=3.999$ , giving us $r\approx4$ .