Volume Formulas For Different Geometric Shapes (2D and 3D Shapes) (2024)
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units. In other words, the volume of any object or container is the capacity of the container to hold the amount of fluid (gas or liquid). The volume of three-dimensional mathematical shapes like cube, cuboid, cylinder, prism and cone etc. can be easily calculated by using arithmetic formulas. Whereas, to find the volumes of complicated shapes, one can use integral calculus.
For example, the volume of the cylinder can be measured using the formula πr2h, where r = d⁄2.
The volume of a rectangular solid is the length times the width times the height. The volume of a sphere is 43 times π times the cube of the radius. The volume of a cylinder is π times the square of the radius times the height. The volume of a cone is 13 times π times the square of the radius times the height.
The volume of a rectangular solid is the length times the width times the height. The volume of a sphere is 43 times π times the cube of the radius. The volume of a cylinder is π times the square of the radius times the height. The volume of a cone is 13 times π times the square of the radius times the height.
Volume of a cube =(side length)^3. Volume of a rectangular prism = length × width × height. Volume of a cylinder = π(radius)^2 × height. Volume of a sphere = (4/3)π(radius)^3.
In this case, the volume of irregular shaped solids can be found by water displacement method: An irregular-shaped solid is dropped into a graduated cylinder filled with water. The volume of the solid is then found by determining the difference between the initial and final readings of the graduated cylinder.
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units.
These shapes have only two dimensions say length and breadth. These are called Three dimensional as they have depth (or height), breadth and length. We can measure their area and Perimeter. We can measure their volume, Curved Surface Area (CSA), Lateral Surface Area (LSA), or Total Surface Area (TSA).
Area of a Rectangle = Length × Breadth. Area of a Triangle = ½ × Base × Height. Area of a Trapezoid = ½ × (Base₁ + Base₂) × Height. Area of a Circle = A = π × r²
Apply the formulas V = l × w × h V = l \times w \times h V=l×w×h and V = b × h V = b \times h V=b×h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
The general equation ax + by + cz + d = 0 represents a plane where a, b and c are constants followed by the condition a, b, c ≠ 0. The equation of the plane passing through the origin is given by ax + by + cz = 0.
Step 1: Find the ratio of the side lengths or dimensions of the two similar solids. Step 2: Cube the ratio from Step 1, which gives the ratio of the volumes of the two similar solids. Step 3: Use the given volume of the solid and the ratio of the volumes from Step 2 to find the volume of the similar solid.
By combining these two steps (area of the bottom of the object and height of the object), we can find the volume of a regularly-shaped object. The area of the bottom (length x width) times the height of the object or L x W x H equals the volume of the object. In this example we used centimeters as our units of length.
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