To calculate the surface area of the toy, we need to find the surface area of the cone and the surface area of the hemisphere separately, and then add them together.
First, let's find the surface area of the cone. The formula for the surface area of a cone is given by A = π * r * (r + l), where r is the radius of the base and l is the slant height of the cone.
Given that the diameter of the base of the cone is 18 cm, the radius is half of the diameter, so the radius of the base is 9 cm.
To find the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height of the cone (12 cm) and the radius of the base (9 cm). Using the Pythagorean theorem, we have:
l^2 = h^2 + r^2
l^2 = 12^2 + 9^2
l^2 = 144 + 81
l^2 = 225
l = √225
l = 15 cm
Now we can calculate the surface area of the cone:
A_cone = π * r * (r + l)
A_cone = π * 9 cm * (9 cm + 15 cm)
A_cone = π * 9 cm * 24 cm
A_cone = 216π cm^2
Next, let's find the surface area of the hemisphere. The formula for the surface area of a hemisphere is given by A = 2πr^2, where r is the radius of the hemisphere.
Since the diameter of the base of the cone is 18 cm, the radius of the hemisphere is half of that, which is 9 cm.
Now we can calculate the surface area of the hemisphere:
A_hemisphere = 2π * (9 cm)^2
A_hemisphere = 2π * 81 cm^2
A_hemisphere = 162π cm^2
Finally, we can find the total surface area of the toy by adding the surface areas of the cone and the hemisphere:
Total surface area = A_cone + A_hemisphere
Total surface area = 216π cm^2 + 162π cm^2
Total surface area = 378π cm^2
So, the surface area of the toy is 378π cm^2.