0

Guest

Courses New

Rotating a curve y=x^1/2 ,[under root x] , about x-axis produces head light as shown. 1)What is the area of disc at any x? 2What is the volume of this head light where x varies from 0 to 2?

Rotating a curve y=x^1/2 ,[under root x] , about x-axis produces  head light as shown. 
 
1)What is the area of disc at any x?
2What is the volume of this head light where x varies from 0 to 2? 

Question Image
Grade:

1 Answers

Venkat
273 Points
5 years ago
1.Area of disc = area of circle = pi*r^2 =
\\A=\pi r^2 \\A=\pi (\sqrt{x})^2 \\A=\pi x
 
  1. consider a small flat disc. The volume of such disc would be
\\V=\pi r^2\times thickness \\ V=\pi (\sqrt{x})^2dx
Add these volumes to get the final volume
\\V=\int_{0}^{2}\pi (\sqrt{x})^2dx \\V=\int_{0}^{2}\pi xdx \\ \\V={\frac{\pi}{2} (x^2)}_{0}^{2} \\ \\V={\frac{\pi}{2} (4)} \\ \\V={2\pi}
 

 

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More