The diagram shows a solid hemisphere of radius 5 cm. find the total surface area of the solid hemisphere.

The answer is 75π

The surface area of the hemisphere (A) is the sum of the half of the surface area of the sphere (A1) and the area of the base which is a circle (A2)
A = 1/2A1 + A2

The surface area of the sphere (A1) with radius r is:
A1 = 4 π r² 

The area of a circular base with radius r is:
A2 = π r²

A = 1/2A1 + A2
A = 1/2 * 4 π r² + π r²
A = 2 π r² + π r²
A = 3 π r²

We know:
r = 5 cm
A = 3 π * 5²
A = 3 π * 25
A = 75π