In mathematics, two-dimensional geometry is focused on the x-y plane; however, when we spin the shapes in 2D geometry, we obtain 3D geometry figures. Three-dimensional geometry is an expansion of two-dimensional mathematics that deals with three axes in the cartesian plane, namely x, y, and z, corresponding to length, breadth, and height. A hemisphere is a three-dimensional figure formed by dividing a sphere along a plane that runs through the sphere's diameter and centre. A hemisphere is just 1⁄2 of a spherical figure.
Volume is the amount of 3D space that an item covers. A bigger volume object takes up more room. The hemisphere can be solid or hollow, and its surface area is measured in square units (like with any other solid form). A hemisphere may be found in everyday objects such as headphones, domes, an igloo, a mushroom, the human brain, and many more. As a result, the volume of a hemisphere is half that of a sphere, which is equal to two-thirds multiplied by pi multiplied by the radius to the power 3.
We know that volume is the number of cubes we can fit inside of a hemisphere. The volume of a hemisphere is also expressed as (unit)3 or cubic units. The cubic meter (m3) is the SI unit of volume, and this is defined as the volume of a hemisphere with a 1-meter diameter. We can also use the United States Centimeter System, which includes inches3, yards3, etc.
The volume of a hemisphere with a radius ‘s’ is determined very easily using the predefined formula and the concept of the volume of the sphere. We know that the volume of a sphere is (4 π s3)/3 since the hemisphere is half of a sphere; therefore, the volume of the hemisphere equals ½ volume of a sphere. This can be formulated as (½ x 4 π s3)/3 or (2 π s3)/3.
We now know that the volume of a hemisphere may be calculated using the formula,
The volume of the hemisphere with radius ‘s’ = 2 π s3/3.
Step 1: Calculate the radius of the hemisphere.
Step 2: With the help of the general formula, calculate the volume of a hemisphere.
If the value of the radius of the sphere is known, then the volume of the hemisphere will be equal to 2 π r3/3.
Step 3: Use cubic units to represent the final solution.
The curved surface area (CSA) of a hemisphere with radius, say 's' can be calculated using the formula mentioned below:
CSA of a hemisphere = 1/2 (The perfect sphere's CSA from which the hemisphere is cut off) = 1/2 (4 π s2) = 2 π s2
The entire surface area, i.e., the area of the curved surface as well as the area of the circular base, produces the total surface area or TSA of a hemisphere.
TSA of a hemisphere = 2 π s2 + π s2 = 3 π s2