Final answer:
To calculate the surface area of a right cone combined with a hemisphere, determine the lateral surface area of the cone and the curved surface area of the hemisphere separately, then sum them together.
Step-by-step explanation:
To find the surface area of a solid which is a right cone and a hemisphere, we need to consider the surface area of each part separately and then combine the results. For the right cone, the surface area consists of the base area, which is a circle, and the lateral surface area, which is a sector of a circle. For the cone, the base area is given by πr² and the lateral surface area is πrl, where r is the radius of the base and l is the slant height of the cone. To find the slant height, if not given, we can use the Pythagorean theorem in a right triangle formed by the slant height (l), the radius of the base (r), and the perpendicular height (h) of the cone.
For the hemisphere, the surface area would normally include the curved part, which is given by 2πr², but since we combine it with the cone which covers the flat surface of the hemisphere, we only need to consider the curved surface area of the hemisphere. Finally, the total surface area of the solid is the sum of the lateral surface area of the cone and the curved surface area of the hemisphere. Thus, if the height of the cone is equal to the diameter of the hemisphere, then we have an elegant symmetry in which the result becomes quite intuitive when considering the geometries together.