Volume of Half Cylinder
The volume of a halfcylinder is defined as the amount of space occupied by the shape in a threedimensional plane. The volume of a halfcylinder is measured in cubic units such as cubic centimeters(cm^{3}), cubic inches(in^{3}), cubic feet(ft^{3}), cubic meters(m^{3}), or simply in cubic units. A halfcylindrical shape in mathematics is a threedimensional solid figure which is obtained when a cylinder is truncated longitudinally. When a horizontal cylinder is cut into two equal pieces parallel to the length of the cylinder, the shapes thus obtained are called halfcylinders. Let us understand the formula to calculate the volume of halfcylinder and partial cylinder in detail in the following sections.
1.  Formula of Volume Of HalfCylinder 
2.  How Do You Find the Volume of Partial Cylinder? 
3.  Formula for Surface Area of Half Cylinder 
4.  FAQs on Volume of HalfCylinder 
Formula of Volume Of HalfCylinder
A halfcylinder in mathematics refers to a threedimensional solid figure which is a longitudinally truncated cylinder. The volume of halfcylinder is equated to half of the total volume of cylinder. The volume of a halfcylinder is defined as the amount of space occupied by a halfcylinder. The volume of a halfcylinder is measured in cubic units, such as cubic centimeters, cubic inches, cubic feet, cubic meters, etc.
The formula to calculate the volume of a halfcylinder can be deduced as,
We know, volume of cylinder = base area × height
⇒ Volume of halfcylinder = πr^{2} × h
where,
 r = Radius
 h = Height
Since, volume of a halfcylinder = (1/2) × volume of cylinder
⇒ Volume of halfcylinder = (1/2) × πr^{2}h
Also, diameter, d = 2 × r
or, r = d/2
Therefore, the volume of a halfcylinder in terms of diameter can be given as,
Volume of halfcylinder = (1/2) × π(d/2)^{2}h = (1/8)πd^{2}h
How Do You Find the Volume of a Partial Cylinder?
A shape of a partial cylinder formed when a cylinder is longitudinally cut by a plane parallel to the sides of the cylinder. Only a partial portion of the cylinder is left whose volume we can find using the following formula:
Volume \(= l(r^2 \text{cos}^{−1}(\dfrac{r − h}{r}) − ( r − h ) \sqrt{ 2 r h − h^2})\)
where,
 r = the radius of the cylinder.
 h = the height of water.
 l = the length of the cylinder.
Note: The cos^{1} function is in radians.
The volume of a partial cylinder will be in cubic units. For example, cubic inches cubic feet, and, cubic meters. Now that we have learned to calculate the volume of a halfcylinder, let us quickly see how to calculate its surface area in the next section.
Formula for the Surface Area of a HalfCylinder
We can calculate the surface area of a halfcylinder by adding half of the curved surface area of the cylinder with an area of two semicircles and the area of the bottom rectangular section. The formula for the surface area of a halfcylinder can be given as,
Total surface area of halfcylinder = (1/2) × curved surface area of a cylinder + 2 × area of semicircle + area of a bottom rectangle
Total surface area of halfcylinder = (1/2) × 2πrh + 2 × (1/2)πr^{2 }+ 2rh
Total surface area of halfcylinder = πrh + πr^{2 }+ 2rh
Let us understand the volume of a halfcylinder better using a few solved examples.
Solved Examples on Volume of Half Cylinder

Example 1: Find the amount of coffee that can be contained in a cup, that is of the shape of a halfcylinder. The radius of the cup is 2 in, while its height is 4 in. (Use π = 3.14)
Solution:
Given:
Radius (r) = 2 in
Height (h) = 4 inWe will use the volume of a halfcylinder formula to find the quantity of coffee the mug can hold.
Volume of a halfcylinder = (1/2)πr^{2}h cubic unitsSubstituting the values in the above formula,
Volume of a halfcylinder = (1/2) × 3.14 × (2)^{2} × (4)Answer: The volume of coffee is 25.12 in^{3}.

Example 2: Sam has a cylindrical candle that is 4 inches in diameter and has a height of 10 inches. He wants to cut it into two halfcylinders. What will be the volume of a half candle? calculate using the volume of the halfcylinder formula. (Use π = 3.14)
Solution:
Given:
Radius of a candle (r) = 2 in
Height of a candle (h) = 10 inLet's use the volume of a halfcylinder formula,
Volume of a halfcylinder = (1/2)πr^{2}h cubic unitsSubstituting the values in the above formula,
Volume of a halfcylindrical candle, V = (1/2) × 3.14 × (2)^{2 }× 10Answer: The volume of halfcylindrical candle is 62.8 in^{3}.
FAQs on the Volume of a HalfCylinder
What Is the Volume of a Half Cylinder?
The volume of a halfcylinder is defined as total space covered by the halfcylinder in a threedimensional plane. The volume of a halfcylinder is equal to half times the volume of a cylinder.
How Do you Find the Volume of a HalfCylinder?
The volume of a halfcylinder can be calculated by dividing the total volume of a cylinder by 2. Given the radius and height of a halfcylinder, we can calculate its volume using the formula, Volume of a cylinder = (1/2)πr^{2}h
where,
 r is the radius
 h is the height of the cylinder
How to Find the Radius of a HalfCylinder Using Volume?
The radius of a halfcylinder can be calculated if the volume and height are known. To find radius in this case, we can apply the volume of a halfcylinder formula, V = (1/2)πr^{2}h, where, "r' is the radius and "h" is the height of the cylinder and substitute the known values to solve for "r".
How Do You Find the Height of a HalfCylinder Using Volume?
The height of a halfcylinder using volume and radius can be calculated by using the formula, Volume of halfcylinder = (1/2)πr^{2}h, where, "r' is the radius and "h" is the height of the cylinder. Substitute the given values and solve to find the missing value of the height of halfcylinder.
How Does the Volume of a Half Cylinder Change When the Radius Is Doubled?
The volume of a halfcylinder is proportional to the square of the radius of the halfcylinder. Therefore, the volume of a halfcylinder becomes four times when the radius is doubled.
What Are the Units of Measurement for the Volume of a HalfCylinder?
The unit of measurement for the volume of a cylinder is cubic units. It can be expressed in units like cm^{3}, in^{3}, ft^{3}, m^{3}, etc.
What Is the Formula for the Surface Area of the HalfCylinder?
The general formula for the total surface area of a halfcylinder is given as, Total surface area of halfcylinder = πrh + πr^{2} + 2r, where "r" is the radius, and "h" is the height of the cylinder.