Answer:
To find the surface area of the toy, we need to find the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone.
Let's first find the radius and slant height of the cone. The height of the cone can be found by subtracting the radius of the hemisphere (6 cm) from the total height of the toy (14 cm). Therefore, the height of the cone is 14 - 6 = 8 cm.
Using the Pythagorean theorem, the slant height of the cone can be found as:
l = sqrt(r^2 + h^2)
where r is the base radius of the cone and h is the height of the cone.
Thus, l = sqrt(6^2 + 8^2) = 10 cm.
Now, we can find the curved surface area of the cone using the formula:
Cone CSA = πrℓ
where r is the base radius of the cone and ℓ is the slant height of the cone.
So, Cone CSA = π × 6 × 10 = 60π cm^2.
Next, let's find the curved surface area of the hemisphere. The formula for the curved surface area of a hemisphere is:
Hemisphere CSA = 2πr^2
where r is the base radius of the hemisphere.
Thus, Hemisphere CSA = 2π × 6^2 = 72π cm^2.
Finally, let's find the area of the circular base of the cone, which is simply πr^2 = π(6^2) = 36π cm^2.
Therefore, the total surface area of the toy is:
Total Surface Area = Cone CSA + Hemisphere CSA + Base Area
Total Surface Area = 60π + 72π + 36π = 168π cm^2.
So, the surface area of the toy is 168π square cm.