Eliminate a component of an equation

Question

评论： Walter Roberson 2021-12-8

%% Q9a
clear;clc;
%1
r=0.1:0.01:100;%m
V=1/3*pi.*power(r,2)*h;%m^3
B=sqrt((r^2)+(h^2));
A=r*pi*B;%m^2

By eliminating ℎ, obtain the expression for 𝐴 as a function of 𝑟 and V.

How should I do that?

Answer 1

Walter Roberson 2021-12-8

V=1/3*pi.*power(r,2)*h;%m^3

If V = something*h then it follows that h = V/something

B=sqrt((r^2)+(h^2));

And that definition for h can be put into B

hHow should I eliminate h and make an expression for A as a function of 𝑟 and V?

Walter Roberson 2021-12-8

Write out the steps by hand, using unresolved symbols. Find the formula, and program the formula in, possibly using vector r values at that time.

If you want to have MATLAB do it, you can use the Symbolic Toolbox --- but it is really straight forward.

B=sqrt((r^2)+(h^2));

implies

B=sqrt((r^2)+((V/(1/3*pi.*power(r,2)))^2));