The volume of a right cylinder is given as V(r,h) =pi*r^2h where r and h are the
ID: 2892147 • Letter: T
Question
The volume of a right cylinder is given as V(r,h) =pi*r^2h where r and h are the radius and height respecitively. Let r* = 1.25 and h* = 3.200 be approximations of r and h respectively by the rounding method. a
a)Determine the absolute error bound of r* and h* respectively.
b)Assuming that pi is exactly 3.14 what is the approximated (absolute) error bound of the cylinder's volume?
c)What is the (absolute) error bounds of h* when h* = 3.2? Is it the same as the one when h* = 3.200?
The volume of right cylinder is given as of as V(r, h) Tr2h. where r and h are the radius and height respectively. Let r 1.25 and h 3.200 be approxima- tions of r and h respectively by the rounding method. a Determine the (absolute) error bounds of r" and h respectively. b ssuming that T is exactly 3.14, what is the approximated (absolute) error bound of the cylin- der's volume? c) What's the (absolute error bounds of h when h" 3.2? Is it the same as the one when 3.200?Explanation / Answer
a) for h* = 3.2 ,r*= 1.25
The error hounds are 0.5 and 0 for r* and h* respectively.
b) pi = 3.14 theb volume V = 3.14 * 1.25^2 * 3 2
V= 15.7
But originally V1 = pi * 1.25 ^2 *3.2
V1 = 15.708
Absolute error = 0.08
c) for h* = 3.2 r= 1.3
Therefore V = pi* 1.3^2 * 3.2 = 16.9897
Absolute error = 1.2897
For h* = 3.200 and r* = 1.250
V= 15.708
Not same as before and therefore error bounds changes.
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