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

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .

Do not assume that the diameter will be half of the diameter of a sphere with volume of . Instead, begin with the sphere with a volume of . Such a simple action will prevent a vexing error!

Thus, we know from our equation for the volume of a sphere that:

Solving for , we get:

If you take the cube-root of both sides, you have:

First, you can factor out an :

Next, factor the :

Which simplifies to:

Thus, the diameter is double that or:

Begin by solving for the length of one side of the cube. Use the formula for surface area to do this:

s= length of one side of the cube

The length of the side of the cube is equal to the diameter of the sphere. Therefore, the radius of the sphere is 3. Now use the formula for the surface area of a sphere:

The surface area of the sphere is .

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .

Do not assume that the diameter will be half of the diameter of a sphere with volume of . Instead, begin with the sphere with a volume of . Such a simple action will prevent a vexing error!

Thus, we know from our equation for the volume of a sphere that:

Solving for , we get:

If you take the cube-root of both sides, you have:

First, you can factor out an :

Next, factor the :

Which simplifies to:

Thus, the diameter is double that or:

Begin by solving for the length of one side of the cube. Use the formula for surface area to do this:

s= length of one side of the cube

The length of the side of the cube is equal to the diameter of the sphere. Therefore, the radius of the sphere is 3. Now use the formula for the surface area of a sphere:

The surface area of the sphere is .

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .

Do not assume that the diameter will be half of the diameter of a sphere with volume of . Instead, begin with the sphere with a volume of . Such a simple action will prevent a vexing error!

Thus, we know from our equation for the volume of a sphere that:

Solving for , we get:

If you take the cube-root of both sides, you have:

First, you can factor out an :

Next, factor the :

Which simplifies to:

Thus, the diameter is double that or:

Begin by solving for the length of one side of the cube. Use the formula for surface area to do this:

s= length of one side of the cube

The length of the side of the cube is equal to the diameter of the sphere. Therefore, the radius of the sphere is 3. Now use the formula for the surface area of a sphere:

The surface area of the sphere is .

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .

Do not assume that the diameter will be half of the diameter of a sphere with volume of . Instead, begin with the sphere with a volume of . Such a simple action will prevent a vexing error!

Thus, we know from our equation for the volume of a sphere that:

Solving for , we get:

If you take the cube-root of both sides, you have:

First, you can factor out an :

Next, factor the :

Which simplifies to:

Thus, the diameter is double that or:

Begin by solving for the length of one side of the cube. Use the formula for surface area to do this:

s= length of one side of the cube

The length of the side of the cube is equal to the diameter of the sphere. Therefore, the radius of the sphere is 3. Now use the formula for the surface area of a sphere:

The surface area of the sphere is .

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .

Do not assume that the diameter will be half of the diameter of a sphere with volume of . Instead, begin with the sphere with a volume of . Such a simple action will prevent a vexing error!

Thus, we know from our equation for the volume of a sphere that:

Solving for , we get:

If you take the cube-root of both sides, you have:

First, you can factor out an :

Next, factor the :

Which simplifies to:

Thus, the diameter is double that or:

Begin by solving for the length of one side of the cube. Use the formula for surface area to do this:

s= length of one side of the cube

The length of the side of the cube is equal to the diameter of the sphere. Therefore, the radius of the sphere is 3. Now use the formula for the surface area of a sphere:

The surface area of the sphere is .

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .

Do not assume that the diameter will be half of the diameter of a sphere with volume of . Instead, begin with the sphere with a volume of . Such a simple action will prevent a vexing error!

Thus, we know from our equation for the volume of a sphere that:

Solving for , we get:

If you take the cube-root of both sides, you have:

First, you can factor out an :

Next, factor the :

Which simplifies to:

Thus, the diameter is double that or:

Begin by solving for the length of one side of the cube. Use the formula for surface area to do this:

s= length of one side of the cube

The length of the side of the cube is equal to the diameter of the sphere. Therefore, the radius of the sphere is 3. Now use the formula for the surface area of a sphere:

The surface area of the sphere is .

The surface area of a sphere is defined by the equation:

For our data, this means:

Solving for , we get:

or

The diameter of the sphere is .