Step 1: Radius of the cone $=$ radius of the hemisphere $=r=5$ cm.
Step 2: Height of the cone $=$ diameter of its base, so
$$h=2r=2\times 5=10\text{ cm}$$
Step 3: Volume of the cone
$$V_{1}=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi(5)^{2}(10)=\frac{250\pi}{3}\text{ cm}^{3}$$
Step 4: Volume of the hemisphere
$$V_{2}=\frac{2}{3}\pi r^{3}=\frac{2}{3}\pi(5)^{3}=\frac{250\pi}{3}\text{ cm}^{3}$$
Step 5: Total volume of the toy
$$V=V_{1}+V_{2}=\frac{250\pi}{3}+\frac{250\pi}{3}=\frac{500\pi}{3}\text{ cm}^{3}$$
Step 6: Substitute $\pi=\dfrac{22}{7}$.
$$V=\frac{500}{3}\times\frac{22}{7}=\frac{11000}{21}=523.81\text{ cm}^{3}$$
Hence the volume of the toy is approximately $523.81$ cm$^{3}$ (i.e. $\dfrac{11000}{21}$ cm$^{3}$).