Let the cost of the ball be \( x \).

According to the problem statement, the bat costs \( 1.00 \) more than the ball. So, the cost of the bat will be \( x + 1.00 \).

Together, the combined cost of the bat and the ball is given as 1.10.
Therefore, the equation summing their costs is:
\[ x + (x + 1.00) = 1.10 \]

Now simplify and solve for \( x \):
\[ 2x + 1.00 = 1.10 \]
\[ 2x = 1.10 - 1.00 \]
\[ 2x = 0.10 \]
\[ x = \frac{0.10}{2} \]
\[ x = 0.05 \]

Thus, the ball costs \(0.05\) or 5 cents.
