High School Math : How to find the volume of a polyhedron

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Find The Volume Of A Polyhedron

Find the volume of the following half cylinder.

Half_cylinder

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a half-cylinder is:

where  is the radius of the base and  is the length of the height.

 

Plugging in our values, we get:

Example Question #2 : How To Find The Volume Of A Polyhedron

Find the volume of the following polyhedron.

Ice_cream_cone

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of the polyhedron is:

Where  is the radius of the cone,  is the height of the cone, and  is the radius of the sphere.

 

Use the formula for a  triangle to find the length of the radius:

 

Plugging in our values, we get:

Example Question #3 : How To Find The Volume Of A Polyhedron

Find the volume of the following polyhedron.

Dome

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of the polyhedron is:

where  is the radius of the cone,  is the height of the cone,  is the radius of the cylinder, and  is the height of the cylinder.

 

Use the formula for a  triangle to find the length of the radius and height of the cone:

 

Plugging in our values, we get:

Example Question #4 : How To Find The Volume Of A Polyhedron

Find the volume of the following polyhedron.

Ice_cream_cone

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of the polyhedron is:

where  is the radius of the polyhedron and  is the height of the cone.

 

Use the formula for a  triangle to find the length of the radius and height:

 

Plugging in our values, we get:

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