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Volume Formulas
The amount of threedimensional space that an object or shape takes up is known as its volume. It is typically expressed in cubic units. In other words, the volume of any object or container refers to the amount of liquid (gas or liquid) it can hold. Arithmetic formulas can be used to quickly compute the volume of threedimensional mathematical forms, including cubes, cuboids, cylinders, prisms, and cones, among others. On the other hand, one can use integral calculus to determine the volumes of complex shapes.
What is Volume Formula?
A mathematical phrase called the Volume Formulas is used to calculate how much space (or vacuum) each threedimensional object takes up overall.
An object’s Volume Formulas is used to determine the total cubic capacity that it can store. Units of volume, or cubic units, are used to indicate a 3dimensional shape’s volume unit.
Volume Formulas of 3D Shapes
The Volume Formulas are now known to be used to compute the volume of a threedimensional object. This part will teach us how to calculate the volumes of various 3D shapes using their corresponding dimensions.
Volume Formula of Cube
When all three sides of a cube are equal in size, the Volume Formulas for a cube depend on those three sides. The area that a cube occupies is known as its volume. The following is the general formula for a cube’s volume:
A cube’s volume is equal to a, a, and a3 cubic units, where an is the cube’s side length.
The Volume Formulas of a cube using the diagonal is V = (3d3)/9, where d is the cube’s diagonal length.
Volume Formula of Cuboid
The volume of a cuboid formula is used to determine the volume of space that the cuboid encloses. Mathematically, a cuboid’s volume can be calculated using the following generic formula:
Cuboid volume is equal to the base area times the height in cubic units.
The cuboid’s base area is equal to l b square units.
Thus, the volume of a cuboid is given by V = l b h = lbh units3, where l b h are the cuboid’s length, breadth, and height.
Volume Formula of Cone
The volume formula for a cone is used to determine how much space is occupied within a 3Dshaped cone with a circular base and a height and radius of r and h, respectively. The cone’s general volume formula is as follows:
A cone’s volume is equal to (1/3)r2h cubic units.
Here,
The cone’s base (circle) has a radius of “r.”
The constant ‘h’, which represents the cone’s height, has a value of either 22/7
Volume Formula of Cylinder
The quantity of space (or capacity) occupied inside the cylinder is calculated using the cylinder’s volume formula. A circle serves as the right circular cylinder’s base, and an rradius circle has a r2radius area. Consequently, the formula for a cylinder’s volume is
A cylinder’s volume is equal to r2h cubic units.
Here,
The cylinder’s base (circle) has a radius of “r.”
H stands for the cylinder’s height.
The value of the constant is either 22/7 (or) 3.142.
Thus, a cylinder’s volume is directly related to both its height and the square of its radius. In other words, if the cylinder’s radius doubles, its volume will increase by a factor of four.
Volume Formula of Sphere
A wonderful illustration of a form that resembles a sphere is a football. It has a circular structure and is a solid object in three dimensions. The volume of a sphere or ball is defined as the volume of air that fills it. The following is the sphere’s volume formula:
The sphere’s volume is (2/3)r2h.
If the sphere’s diameter equals 2r
Therefore, the sphere’s volume is equal to (2/3)r2h = (2/3)r2(2r) = (4/3)r3 cubic units.
A sphere has a volume of (4/3)r3 cubic units.
Here,
The sphere’s height (h) and radius (r) are both constants with values of either 3.142 or 22/7.
Volume Formula of Hemisphere
Since a hemisphere is half of a sphere, calculate its volume using the sphere’s volume formula. Now take into account that a sphere has a radius of ‘r’ units and a volume of (4/3)r3.
As a result, the formula for the hemisphere’s volume is: V = ½ (4/3)πr3
Hemisphere’s volume is equal to (2/3)r3 cubic units.
Here,
The hemisphere’s radius, or “r,” has a constant value of either 3.142 or 22/7.
Volume Formula of Prism
The product of the base’s area and the prism’s height provides the volume formula for prisms. It is written mathematically as:
Prism volume is given by V = B h units3.
Here,
Base area in square units is “B.”
The prism’s height is expressed in units as “h.”
Based on how the bases of prisms are shaped, there are seven different varieties of prisms. The various prism bases have an impact on the volume formula for prisms. To get the idea behind the volume formulas for various prisms, look at the volume of prisms.
Volume Formula of Pyramid
A pyramid’s volume is equivalent to onethird of a prism’s volume (i.e., their bases and heights are congruent). Thus,
The pyramid’s volume (V) equals 13 (Bh) units3, where
B is the pyramid’s base area measured in square units.
h is the pyramid’s height in units of altitude.
Examples on Volume Formula
Extramarks is a studentcentered digital learning platform. With the aid of the Extramarks website, students are free to learn in the manner that best suits them. The Volume Formulas examples provide students with the assurance they need to perform better on the CBSE exam, along with a range of exercises and problem sets. The solved examples on the Volume Formulas are available from Extramarks to help students study the material properly. Utilizing the Volume Formulas is the first step in exam preparation. They must review the concept because it is a critical one.
Reviewing the Volume Formulas examples is essential because it is one of the best approaches to assisting students in developing their skills. Students gain from using the Extramarks website by strengthening the fundamental concepts presented in the course material and by enhancing their conceptual knowledge. The solved examples in the Volume Formulas were created to aid students in quickly improving their abilities. For students who may find the questions difficult, Extramarks’ Volume Formulas are accessible to aid in chapter practice.
Since solved examples on the Volume Formulas are recommended in exams, students should practice them in order to get an idea of how questions may appear in their examination. Students can find a variety of the Volume Formulas on the Extramarks website to aid them in achieving good exam scores. For students who require assistance with the Volume Formulas, the Extramarks website is a dependable substitute. Students can find solved examples on Extramarks, a reputable website, to aid them in their examination preparation. Students should trust Extramarks to provide them with accurate solved examples.
The key concepts for students are organised in the Volume Formulas solved examples provided at the Extramarks’ website so that they will not have any trouble understanding the material. Using Extramarks and its Volume Formulas solved examples provides a number of advantages because it enables flexible study. Students, for instance, can learn whenever they want and from any location. Using this online tool, students can practice the Volume Formulas solved examples. Students do not need to go elsewhere for trustworthy examples because the Extramarks website offers credible solutions.
In order to gain a sense of the types of questions that have appeared in past years, students should be familiar with the Extramarks website and previous years’ papers provided on the Extramarks website. Since the examination often covers the same topics, students should carefully analyse the Volume Formulas solved examples and the practice papers for a better understanding and excellent grades. Volume Formulas solved examples on the Extramarks website guide students through the chapter summary.These solutions were created by Extramarks professionals and are laid out in a stepbystep manner. Students can easily understand the concepts in the chapter with the help of the solved examples. The solved examples are created by the subject matter experts at the Extramarks’ website. Therefore, the Volume Formulas examples provided are reliable and trustworthy.
FAQs (Frequently Asked Questions)
1. What does the volume of a 1/3 mean?
The equation pi r2 h gives the volume of a cylinder. Three cones with the same height can fit inside of a cylinder, according to math. This logically implies that if three cones can fill a cylinder’s volume, then a cone’s volume equals onethird of a cylinder with the same height.
2. What is the liquid's volume?
The volume of liquid that a vessel contains is measured in standard units as the liquid measurement. It is sometimes referred to as the vessel’s “volume” or “capacity.” Juice bottle with a 1 litre capacity and a baby milk bottle with millilitre measuring indications.