# Derive the Volume of a Sphere using Calculus

## Homework Statement

Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong.

## Homework Equations

Integrating a circle of radius r at angle θ (Theta)

## The Attempt at a Solution #### Attachments

Orodruin
Staff Emeritus
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i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong.

Also, you should make the effort of typing out your attempt if you want people to help you.

LCKurtz
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Gold Member
Your error is using ##ds## for the thickness of your disk. It should be ##dy=R\cos\theta d\theta##.

• Shivam
Dick
Homework Helper

## Homework Statement

Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong.

## Homework Equations

Integrating a circle of radius r at angle θ (Theta)

## The Attempt at a Solution

I can see your attempted solution. The problem is with ##ds=Rd\theta##. That is arc length along the surface of the sphere. It is not the same as the thickness of your circular section. Can you correct it?

## Homework Statement

Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong.

## Homework Equations

Integrating a circle of radius r at angle θ (Theta)

## The Attempt at a Solution

Your error is using ##ds## for the thickness of your disk. It should be ##dy=R\cos\theta d\theta##.
I got the correct answer by using the correcct thickness you gave me , but i still don't know how did you get that, can you explain please.

Dick
Homework Helper
I got the correct answer by using the correcct thickness you gave me , but i still don't know how did you get that, can you explain please.

The thickness is the vertical thickness of the slice. The arc length you have is not vertical, it's tangent to the sphere. So it makes a varying angle with the vertical as you move up the sphere. Use trig to turn that into a vertical distance.

• Shivam
Your error is using ##ds## for the thickness of your disk. It should be ##dy=R\cos\theta d\theta##.

Can you show me how did you get that, i thought all day but i can't get it.

haushofer
• 