Answered step by step
Verified Expert Solution
Question
1 Approved Answer
Let A R 3 be Jordan-measurable in R 3 . Define the function a: R [0, ) by a(h) = 2 ({(x, y) R 2
Let A R 3 be Jordan-measurable in R 3 . Define the function a: R [0, ) by a(h) = 2 ({(x, y) R 2 | (x, y, h) A}), that is, the area of {(x, y) R 2 | (x, y, h) A}, for all h R. 1. Justify that a is well-defined. 2. Let h1 = inf{h R | a(h) > 0} and h2 = sup{h R | a(h) > 0}. Show that if the restriction of a to [h1, h2] is a polynomial of degree at most 3, then the volume of A is given by 3 (A) = h2 h1 6 a(h1) + a(h2) + 4a h1 + h2 2 . 3. Using the above formula, find the volume of a cone of height H > 0 and base area B > 0.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started