Curved Surface Area of a Hemisphere

The curved surface area of a hemisphere is the space occupied by the curved surface of the hemisphere. The surface area of a three-dimensional object is defined as the space occupied by the surface of the object. A hemisphere is obtained when a sphere is cut along a plane passing through the center of the sphere. In other words, a hemisphere is half of a sphere. In this section, we will discuss the curved surface area of a hemisphere along with solved examples.

Curved surface area of a hemisphere is defined as the area covered by the curved surface. In other words, the area of the outer surface of the hemisphere. The curved surface area of the hemisphere is expressed in square units, using units like m², cm², ft², yd², etc.

The curved surface area of a hemisphere is the area of its curved surface. For a hemisphere, if its radius is given, then its curved surface area can be given by:
Curved surface area of a hemisphere = 1/2 (Curved surface area of a sphere) = 1/2 (4 π r²) = 2 π r², where r is the radius of the hemisphere

As we learned in the previous section, the curved surface area of a hemisphere is 2πr². Thus, we follow the steps shown below to find the curved surface area of a hemisphere.

• Step 1: Identify the radius of the hemisphere and name it to be 'r'.
• Step 2: Find the curved surface area of a hemisphere using the formula = 2πr².
• Step 3: Represent the final answer in square units.

Example: Find the curved surface area of a hemisphere having radius = 7 units. (Use π = 22/7)

Solution:

Radius of the hemisphere = 7 units
Curved surface area of a hemisphere = 2πr² = 2 (22/7 7² = 2 × 22 × 7 = 308 units²

Therefore, the curved surface area of the hemisphere = 308 units²

Now that we've understood the formula and method to calculate the curved surface area of hemisphere, let us have a look at a few solved examples for better understanding.

Related Topics

Listed below are a few topics related to the curved surface area of hemisphere, take a look.

• Volume of Hemisphere
• Sphere
• Volume of Sphere
• Surface Area of Sphere

What is Meant by the Curved Surface Area of Hemisphere?

The curved surface area of a hemisphere is defined as the area covered by the curved surface of a hemisphere. A hemisphere is a 3-D shape that is obtained when a sphere is cut along a plane passing through the center of the sphere. In other words, a hemisphere is half of a sphere.

What is the Formula Curved Surface Area of a Hemisphere?

The curved surface area of a hemisphere can be calculated using the given radius. For a hemisphere, if its radius (r) is given, then its total surface area can be given by, Curved Surface Area = 2 π r²

How Do You Find the Curved Surface Area of a Hemisphere?

The curved surface area of a hemisphere can be calculated using the following steps,

• Note down the radius of the hemisphere, 'r'.
• Apply the formula to calculate the curved surface area, CSA of hemisphere = 2 π r²
• Express the answer in square units.

What are the Units Used to Express the Curved Surface Area of a Hemisphere?

In measurements, we express the curved surface area of the hemisphere in square units. Some common units are square meters, square inches, square centimeters, etc.

What is the Curved Surface Area of a Hollow Hemisphere?

The curved surface area of a hollow hemisphere can be calculated using the formula, CSA of hollow sphere = 2π r\(_2\)² + 2πr\(_1\)², where, r\(_1\) is the radius of the internal hemisphere, and r\(_2\) is the radius of the external hemisphere.

What is the Difference Between Total Surface Area of and Curved Surface Area of Hemisphere?

Curved surface area of hemisphere is the area covered by the curved surface of a hemisphere, whereas total surface area is space covered by the curved surface and the base surface of the hemisphere in 2-D plane.