Common Core: High School - Geometry : High School: Geometry

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #43 : Geometric Measurement & Dimension

Find the radius of a hemisphere, where the volume is
Round your answer to  digits.

Possible Answers:

Correct answer:

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

Since we are given the volume (), we can plug it into the equation.

Now we can solve for .

Now we divide by on each side.

Now our equation is

To solve for , we need to take the cube root on each side.

Here is a picture representation of the hemisphere.

Plot5

Example Question #5 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Find the radius of a hemisphere, where the volume is .
Round your answer to  digits.

Possible Answers:

Correct answer:

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

Since we are given the volume (), we can plug it into the equation.

Now we can solve for .

Now we divide by  on each side.

Now our equation is

To solve for , we need to take the cube root on each side.

Here is a picture of what the hemisphere look like.

Plot7

Example Question #44 : Geometric Measurement & Dimension

Find the radius of a hemisphere, where the volume is .
Round your answer to  digits.

Possible Answers:

Correct answer:

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

Since we are given the volume (), we can plug it into the equation.

Now we can solve for .

Now we divide by  on each side.

Now our equation is

To solve for , we need to take the cube root on each side.

Here is a picture of the hemisphere.

 

Plot8

Example Question #45 : Geometric Measurement & Dimension

Find the radius of a sphere, where the volume is .
Round your answer to  digits.

Possible Answers:

Correct answer:

Explanation:

Before we find the radius of a sphere, we need to recall the equation.

Since we are given the volume (), we can plug it into the equation.

Now we can solve for .

Now we divide by  on each side.

Now our equation is

To solve for , we need to take the cube root on each side.

Here is a picture of the sphere.

Plot9

Example Question #46 : Geometric Measurement & Dimension

Find the radius of a sphere, where the volume is .
Round your answer to  digits.

 

Possible Answers:

Correct answer:

Explanation:

Before we find the radius of a sphere, we need to recall the equation.

Since we are given the volume (), we can plug it into the equation.

Now we can solve for .

Now we divide by on each side.

Now our equation is

To solve for , we need to take the cube root on each side.

Here is a picture of the sphere.

Plot10

Example Question #42 : Geometric Measurement & Dimension

Find the radius of a hemisphere, where the volume is .
Round your answer to  digits.

Possible Answers:

Correct answer:

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

Since we are given the volume (), we can plug it into the equation.

Now we can solve for .

Now we divide by  on each side.

Now our equation is

To solve for , we need to take the cube root on each side.

Here is a picture of the hemisphere.

Plot11

Example Question #1 : Identify Shapes In 2 D Cross Sections And Rotations In 3 D: Ccss.Math.Content.Hsg Gmd.B.4

Given a cylinder with radius  and height  find the area of a cross section that's parallel to its base. Round your answer to the nearest tenth.

Possible Answers:

Correct answer:

Explanation:

The first step is see what the cross section parallel to the base looks like.

Since we are dealing with a cylinder, the cross section that we are dealing with parallel to the base is a circle.

So all we need to do is recall the area of a circle equation, and substitute the radius given for .

Now we round our answer to the nearest tenth

Example Question #1 : Identify Shapes In 2 D Cross Sections And Rotations In 3 D: Ccss.Math.Content.Hsg Gmd.B.4

Given a sphere with a volume of  find the area of the perpendicular cross section right through its center. Round your answer to the nearest tenth.

 

Possible Answers:

Correct answer:

Explanation:

The first step is to recall the volume equation of a sphere.

Since we are given the volume, we can plug it in for V

Since we want to find the area of the perpendicular cross section, we need to find what the radius is.

Now we solve for 

Now we can use the radius we found to find the area of the cross section.

The cross section in this case is a circle, so now we will use the area of a circle formula, which is

Now we simply substitute the radius we just found for .

Now we round our answer to the nearest tenth, which is

Example Question #2 : Identify Shapes In 2 D Cross Sections And Rotations In 3 D: Ccss.Math.Content.Hsg Gmd.B.4

Given a sphere with a volume of  find the area of the perpendicular cross section right through its center. Round your answer to the nearest tenth.

 

Possible Answers:

Correct answer:

Explanation:

The first step is to recall the volume equation of a sphere.

Since we are given the volume, we can plug it in for V

Since we want to find the area of the perpendicular cross section, we need to find what the radius is.

Now we solve for r

Now we can use the radius we found to find the area of the cross section.

The cross section in this case is a circle, so now we will use the area of a circle formula, which is

Now we simply substitute the radius we just found for .

Now we round our answer to the nearest tenth, which is

Example Question #3 : Identify Shapes In 2 D Cross Sections And Rotations In 3 D: Ccss.Math.Content.Hsg Gmd.B.4

Given a sphere with a volume of  find the area of the perpendicular cross section right through its center. Round your answer to the nearest tenth.

 

Possible Answers:

Correct answer:

Explanation:

The first step is to recall the volume equation of a sphere.

Since we are given the volume, we can plug it in for V

Since we want to find the area of the perpendicular cross section, we need to find what the radius is.

Now we solve for r

Now we can use the radius we found to find the area of the cross section.

The cross section in this case is a circle, so now we will use the area of a circle formula, which is

Now we simply substitute the radius we just found for .

Now we round our answer to the nearest tenth, which is

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept
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