Last updated on July 31st, 2025
A half sphere, or hemisphere, is a 3-dimensional shape that is half of a full sphere. The surface area of a hemisphere includes both its curved surface and its flat circular base. In this article, we will learn about the surface area of a half sphere.
The surface area of a half sphere is the total area occupied by the outer surface of a hemisphere. It is measured in square units.
A hemisphere is formed by slicing a sphere into two equal halves, resulting in a curved surface and a flat circular base.
The surface area of a hemisphere includes both the curved surface area and the total surface area.
A half sphere has a curved surface and a flat circular base. Look at the hemisphere below to see its surface area and radius(r).
A half sphere has two types of surface areas:
Curved Surface Area of a Half Sphere
Total Surface Area of a Half Sphere
The area of the curved part of the hemisphere, excluding its base, is known as the curved surface area of a half sphere.
The formula for the CSA (Curved Surface Area) of a hemisphere is given as: Curved Surface Area = 2𝜋r² square units
Here, r is the radius of the base of the hemisphere.
The total area occupied by the half sphere, including the area of the curved surface and the area of the circular base, is known as the total surface area of a half sphere.
The total surface area of a half sphere is calculated using the formula: Total surface area = 3𝜋r² square units Where r is the radius of the base of the hemisphere.
The total surface area of a half sphere = base area of a half sphere + curved surface area of a half sphere.
Here, the base area of a half sphere = 𝜋r²
Curved surface area of a half sphere = 2𝜋r²
Substituting the formulas into the total surface area,
Total surface area of a half sphere, T = 𝜋r² + 2𝜋r²
Therefore, the total surface area of a half sphere T = 3𝜋r²
The volume of a half sphere shows how much space is inside it. It tells us how much space the half sphere can hold. The volume of a half sphere can be found using the formula: Volume = (2/3)𝜋r³ (cubic units)
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a half sphere are the same. This confusion arises because both involve the radius. Always remember that CSA covers only the curved side of the half sphere, and TSA includes the curved surface and the base.
Given r = 7 cm. Use the formula: CSA = 2𝜋r² = 2 × (22/7) × 7 × 7 = 2 × 22 × 7 = 308 cm²
Find the total surface area of a half sphere with a radius of 5 cm.
TSA = 235.5 cm²
Use the formula: TSA = 3𝜋r² = 3 × 3.14 × 5 × 5 = 3 × 3.14 × 25 = 3 × 78.5 = 235.5 cm²
A half sphere has a radius of 6 cm. Find the total surface area.
TSA = 339.12 cm²
Use the TSA formula: TSA = 3𝜋r² = 3 × 3.14 × 6 × 6 = 3 × 3.14 × 36 = 3 × 113.04 = 339.12 cm²
Find the curved surface area of a half sphere with a radius of 3.5 cm.
CSA = 77 cm²
CSA = 2𝜋r² = 2 × (22/7) × 3.5 × 3.5 = 2 × 22 × 0.5 × 3.5 = 22 × 3.5 = 77 cm²
The curved surface area of a half sphere is 660 cm². Find the radius.
Radius = 10.5 cm
Students often make mistakes while calculating the surface area of a half sphere, leading to wrong answers. Below are some common mistakes and the ways to avoid them.
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