$24 \cdot 10$ If a spherical shell "coat" is uniformly wrapped around a sphere of radius $R$, and if the volume of the "coat" is equal to the volume of the sphere, the thickness of the spherical shell "coat" is
(A) $(\sqrt[3]{3}-1) R$.
(B) $\sqrt[3]{3} R$.
(C) $\sqrt[3]{2} R$.
(D) $(\sqrt[3]{2}-1) R$.
(2nd "Hope Cup" National Mathematics Invitational, 1991)
[Solution] Let the radius of the spherical shell be $R+x$. According to the problem, we have

that is
$$
\frac{4}{3} \pi(R+x)^{3}=2\left(\frac{4}{3} \pi R^{3}\right) \text {, }
$$

which gives
$$
(R+x)^{3}=2 R^{3} \text {, }
$$

thus the correct choice is $(D)$.