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# Category Archives: Spherical Coordinates

## Geometric Formula PROOF Integration problems

## Area of a Triangle Formula Proof example question

Use Integration techniques in order to derive the formula for the Area of a Triangle, *A*, such that

where *b* is the base and *h* is the height.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Area of a Trapezoid Formula Proof example problem

Use Integration to derive the formula for the Area of a Trapezoid, *A*, such that

where *b*_{1} and *b*_{2} are bases and *h* is the height.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Area of a Circle Formula Proof example

Use Integration to derive the formula for the Area of a Circle, *A*, such that

where *r* is the radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Area of a Circle Formula Proof example question

Use **Double** Integration to prove the formula for the Area of a Circle, *A*, such that

where *r* is the radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Sphere Formula Proof example problem

Use the **Disk** Integration method to derive the formula for the Volume of a Sphere, *V*, such that

where *r* is the radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Cone Formula Proof example

Use the **Disk** Integration method to prove the formula for the Volume of a Right Circular Cone, *V*, such that

where *r* is the radius and *h* is the height.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Torus Formula Proof example question

Use the **Washer** Integration method to derive the formula for the Volume of a Torus, *V*, such that

where *r* is the **inner** (minor) radius and *R* is the **outer** (major) radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Torus Formula Proof example problem

Use the **Shell** Integration method to prove the formula for the Volume of a Torus, *V*, such that

where *r* is the **inner** (minor) radius and *R* is the **outer** (major) radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Surface Area of a Cone Formula Proof example

Use Integration to derive the formula for the Lateral Surface Area of a Right Circular Cone, *S _{A}*, such that

where *r* is the radius and *h* is the height.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Surface Area of a Right Circular Cone Formula Proof with Double Integration example problem

Use **Double** Integrals to derive the formula for the Lateral Surface Area of a Right Circular Cone, *S _{A}*, where

where *r* is the radius and *h* is the height.

Solution to this **Calculus Geometric Formula Proof** practice problem is provided in the video below!

## Surface Area of a Sphere Formula Proof example question

Use Integration to prove the formula for the Surface Area of a Sphere, *S _{A}*, such that

where *r* is the radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Torus Formula Proof example

Use the **Cylindrical Coordinates** (Triple Integration) method to prove the formula for the Volume of a Torus, *V*, such that

where *r* is the **inner** (minor) radius and *R* is the **outer** (major) radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Sphere Formula Proof example question

Use the **Spherical Coordinates** (Triple Integration) method to derive the formula for the Volume of a Sphere, *V*, such that

where *r* is the radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Cone Formula Proof example problem

Use the **Spherical Coordinates **(Triple Integration) method to derive the formula for the Volume of a Right Circular Cone, *V*, such that

where *r* is the radius and *h* is the height.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

## Volume of a Torus Formula Proof example

Use the **Spherical Coordinates** (Triple Integration) method to prove the formula for the Volume of a Torus, *V*, such that

where *r* is the **inner** (minor) radius and *R* is the **outer** (major) radius.

Solution to this **Calculus Geometric Formula Proof** practice problem is given in the video below!

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