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A whiffle ball like surface $S$ is the portion of the sphere:

$$x^2+y^2+z^2=9$$

...where:

$$x^2+y^2\geq 1, \, x^2+z^2\geq 1, \, y^2+z^2\geq 1$$

$12\pi(3-2\sqrt{2})$

$9\pi(3-2\sqrt{2})$

$12\pi(\sqrt{2}-1)$

$72\pi(\sqrt{2}-1)$

$6\pi(3-2\sqrt{2})$