You are here:

Calculus/Rectangle Bounded by semicircle

Advertisement

Expert: - 9/22/2008


Question
I am having trouble even getting started on this problem...   A rectangle is bounded by the x-axis and the semicircle y=sqrt(36-xsquared). Write the area of the rectangle as a function of x, and determine domain of the function. (Assume rectangle is symmetric about y-axis).

Answer

Semicircle
Questioner:   Braden
Category:  Calculus
Private:  No
 
Subject:  Rectangle Bounded by semicircle
Question:  I am having trouble even getting started on this problem...   A rectangle is bounded by the x-axis and the semicircle y=sqrt(36-xsquared). Write the area of the rectangle as a function of x, and determine domain of the function. (Assume rectangle is symmetric about y-axis).
......................................
Hi, Braden,

Try a diagram: (see attached.)


So the base is 2x and the height is  y = sqrt(36 - x^2).
Obviously  0 <= x <= 6


That should do it.

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

©2012 About.com, a part of The New York Times Company. All rights reserved.