Jawaban:

To find the surface area of the figure, we need to find the area of the cone and the area of the hemisphere, and then add them together.

Area of the cone:

We know the slant height of the cone is 10 cm, and the diameter is 12 cm. So, the radius of the cone is 6 cm (half of the diameter). We can use the Pythagorean theorem to find the height of the cone:

10^2 = 6^2 + h^2

100 = 36 + h^2

h^2 = 64

h = 8

So, the height of the cone is 8 cm. The formula for the surface area of a cone is:

A = πrℓ + πr^2

where r is the radius of the base of the cone, ℓ is the slant height, and π is approximately 3.14.

Plugging in our values, we get:

A = π(6)(10) + π(6)^2

A = 188.4 cm^2

Area of the hemisphere:

The diameter of the hemisphere is also 12 cm, so the radius is 6 cm. The formula for the surface area of a hemisphere is:

A = 2πr^2

Plugging in our value, we get:

A = 2π(6)^2

A = 226.08 cm^2

Total surface area:

Adding the area of the cone and the area of the hemisphere, we get:

A = 188.4 + 226.08

A = 414.48 cm^2

So, the surface area of the figure is 414.48 cm^2.