Geometry Geometry Math Forum

July 5th, 2018, 12:04 AM   #1
Senior Member

Joined: Nov 2010
From: Indonesia

Posts: 2,001
Thanks: 132

Math Focus: Trigonometry

A water pipe whose diameter is 84 cm and length is 2,4 m can contain rain water with the water height 68 cm like in the attached picture.

Determine:
a. The surface area which gets contact with the water
b. The volume of the water (in liters)

So... How do I do? What is the simple way to determine the area of a... truncated circle? (Don't know what the proper term is.)
Attached Images Water Pipe.JPG (12.3 KB, 0 views)

Last edited by skipjack; July 5th, 2018 at 10:52 AM. July 5th, 2018, 04:42 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Looks like a pretty standard Calculus II problem. Start by drawing a cross section of the pipe on a coordinate system- a circle with center at (0, 0) and diameter 84, so radius 42, has equation $\displaystyle x^2+ y^2= 42^2$. The bottom of that circle is at y= -42, the top is at y= 42. The surface of the water is a horizontal line at y= 68- 42= 26. At every y, a horizontal line intersects the circle at $\displaystyle x= \pm \sqrt{42^2- y^2}$ so has length $\displaystyle 2\sqrt{42^2- y^2}$. Taking a 'thickness' of $\displaystyle \Delta y$, the area of that thin horizontal strip is $\displaystyle 2\sqrt{42^2- y^2}\Delta y$. Adding those gives the Riemann sum, $\displaystyle \sigma 2\sqrt{42^2- y^2}\Delta y$, that, in the limit, is the integral for the area, $\displaystyle 2\int_{-42}^{26}\sqrt{42^2- y^2}dy$. July 5th, 2018, 11:10 AM #3 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 A "truncated circle" is called a circular segment, and has a standard area formula that can be used for part b. July 5th, 2018, 05:59 PM #4 Senior Member   Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry Looks like 9 graders wouldn't be able to solve this after all... Tags pipe, water Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ganesh Ujwal Physics 2 January 3rd, 2015 07:47 AM Chikis Elementary Math 15 October 17th, 2014 09:30 PM burgess Elementary Math 9 July 21st, 2014 03:07 AM r-soy Physics 1 December 15th, 2013 03:54 PM johnny Physics 7 October 28th, 2007 04:29 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      