Volume of solids of revolution: the cone. Part 3. Full article at: http://www.firsttimeprogrammer.blogspot.com/2015/03/volume-of-solids-of-revolution-cone.html

solid_of_revolution3.R

# Solid of rotation: a cone
#-------------------------------------------------------------------------------

# Our function to generate the solid of rotation
foo <- function(x)
{
    return(0.5*x)
}

# This function integrates f^2 over the given [a,b] interval
# Assuming we're using only the positive half of the real line.
integrate <- function(f,a,b,dx=0.001)
{
    if(a > b)
    {
        print('Please make sure b > a then enter again.')
        return(0)
    }else if(a == b)
    {
        return(0)
    }
    
    partial_sum = 0
    
    while(a < b)
    {
        partial_sum <- partial_sum + max(f(a)^2,f(a+dx)^2)*dx
        a <- a + dx
    }
    
    return(partial_sum)
}



# Formula for the volume of a cone and comparison with the estimatation
cone_volume <- function(r,h,compare=T)
{
    v <- pi*h*r^2/3
    
    if(!compare)
    {
        return(v)
    }else
    {
        v2 <- pi*integrate(foo,0,h)
        error <- abs(v - v2)/v*100
        print(paste('We missed of:',error,'%'))
        string_tp <- c(v,v2)
        names(string_tp) <- c('Real volume','estimated volume')
        print(string_tp)
    }
}


# Let's approximate the volume
cone_volume(5,10)