Find the curved surface area and total surface area of a hollow hemisphere whose outer and inner radii are 4.2 cm and 2.1 cm respectively.

Given : Inner radius of hollow hemisphere = r_int = 2.1 cm

Outer radius of hollow hemisphere = r_ext = 4.2 cm

To find : CSA of hollow hemisphere = ?

TSA of hollow hemisphere = ?

Formula : CSA of hemisphere = 2r²

TSA of hemisphere = r²

Solution : Outer surface area = CSA_ext = 2r_ext² = 2 × 4.2 × 4.2 = 35.28 cm²

Inner surface area = CSA_int = 2r_int² = 2 × 2.1 × 2.1 = 8.82 cm²

Area of the edges = (r_ext² – r_int²) = (4.2² – 2.1²) = 13.23 cm²

Curved surface area of hollow hemisphere = CSA_ext + CSA_int = 35.28 + 8.82 = 44.1 cm²

Total surface area of hollow hemisphere = CSA + Area of edges = 44.1 + 13.23 = 57.33 cm²

∴ The curved surface area and total surface area of the hollow cylinder is 44.1 cm² and 57.33 cm² respectively.