how big are 1000 double?

i an learning c++ and in one lesson was a code which is about exception handling. My question to this code is actually: is the output and calculation of the memory size correct? When I allocate a block of memory with new double(1000), isn't the size then 8000bytes ?

The "cerr" only counts as 1kB instead of 8kB. Am i wrong?

Thanks a lot for any answer

i got the size of 1 double with getsizeof(doulbe) to confirm it is 8Bytes.

#include <iostream>
#include <cstdlib>
#include <new>
using namespace ::std;
int main()
{
    int i = 0;
    double *q;

try
{
    while (1)
    {
        q = new double[1000];
        i++;
    }
}
catch (bad_alloc &ex)
{
    cerr << "The memory is used up.  " << i
         << " Kilobyte were available." << endl;
    exit(1);
}
}