Volume of Half Cylinder
The volume of a half-cylinder is defined as the amount of space occupied by the shape in a three-dimensional plane. The volume of a half-cylinder is measured in cubic units such as cubic centimeters(cm3), cubic inches(in3), cubic feet(ft3), cubic meters(m3), or simply in cubic units. A half-cylindrical shape in mathematics is a three-dimensional 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 half-cylinders. Let us understand the formula to calculate the volume of half-cylinder and partial cylinder in detail in the following sections.
| 1. | Formula of Volume Of Half-Cylinder |
| 2. | How Do You Find the Volume of Partial Cylinder? |
| 3. | Formula for Surface Area of Half Cylinder |
| 4. | FAQs on Volume of Half-Cylinder |
Formula of Volume Of Half-Cylinder
A half-cylinder in mathematics refers to a three-dimensional solid figure which is a longitudinally truncated cylinder. The volume of half-cylinder is equated to half of the total volume of cylinder. The volume of a half-cylinder is defined as the amount of space occupied by a half-cylinder. The volume of a half-cylinder is measured in cubic units, such as cubic centimeters, cubic inches, cubic feet, cubic meters, etc.
The formula to calculate the volume of a half-cylinder can be deduced as,
We know, volume of cylinder = base area × height
⇒ Volume of cylinder = πr2 × h
where,
- r = Radius
- h = Height
Since, volume of a half-cylinder = (1/2) × volume of cylinder
⇒ Volume of half-cylinder = (1/2) × πr2h
Also, diameter, d = 2 × r
or, r = d/2
Therefore, the volume of a half-cylinder in terms of diameter can be given as,
Volume of half-cylinder = (1/2) × π(d/2)2h = (1/8)πd2h
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 half-cylinder, let us quickly see how to calculate its surface area in the next section.
Formula for the Surface Area of a Half-Cylinder
We can calculate the surface area of a half-cylinder by adding half of the curved surface area of the cylinder with an area of two semi-circles and the area of the bottom rectangular section. The formula for the surface area of a half-cylinder can be given as,
Total surface area of half-cylinder = (1/2) × curved surface area of a cylinder + 2 × area of semicircle + area of a bottom rectangle
Total surface area of half-cylinder = (1/2) × 2πrh + 2 × (1/2)πr2 + 2rh
Total surface area of half-cylinder = πrh + πr2 + 2rh
Let us understand the volume of a half-cylinder better using a few solved examples.
FAQs on the Volume of a Half-Cylinder
What Is the Volume of a Half Cylinder?
The volume of a half-cylinder is defined as total space covered by the half-cylinder in a three-dimensional plane. The volume of a half-cylinder is equal to half times the volume of a cylinder.
How Do you Find the Volume of a Half-Cylinder?
The volume of a half-cylinder can be calculated by dividing the total volume of a cylinder by 2. Given the radius and height of a half-cylinder, we can calculate its volume using the formula, Volume of a cylinder = (1/2)πr2h
where,
- r is the radius
- h is the height of the cylinder
How to Find the Radius of a Half-Cylinder Using Volume?
The radius of a half-cylinder can be calculated if the volume and height are known. To find radius in this case, we can apply the volume of a half-cylinder formula, V = (1/2)πr2h, 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 Half-Cylinder Using Volume?
The height of a half-cylinder using volume and radius can be calculated by using the formula, Volume of half-cylinder = (1/2)πr2h, 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 half-cylinder.
How Does the Volume of a Half Cylinder Change When the Radius Is Doubled?
The volume of a half-cylinder is proportional to the square of the radius of the half-cylinder. Therefore, the volume of a half-cylinder becomes four times when the radius is doubled.
What Are the Units of Measurement for the Volume of a Half-Cylinder?
The unit of measurement for the volume of a cylinder is cubic units. It can be expressed in units like cm3, in3, ft3, m3, etc.
What Is the Formula for the Surface Area of the Half-Cylinder?
The general formula for the total surface area of a half-cylinder is given as, Total surface area of half-cylinder = πrh + πr2 + 2rh, where "r" is the radius, and "h" is the height of the cylinder.