Volume Calculator
Volume Calculator helps to find the volume for a given shape like a sphere, cube, cylinder, cone, cuboid, triangular prism, or triangular pyramid. Volume can be defined as the total space that is enclosed within a three-dimensional closed shape. The SI unit of volume is cubic meter.
What is Volume Calculator?
Volume Calculator is an online tool used to calculate the volume of a three-dimensional shape. Suppose we have a bottle that can hold 50 cm3 of water up to the brim. Then the volume of the bottle will be 50cm3. To use the volume calculator, choose the shape from the drop-down menu and enter values in the input box.
Volume Calculator
How to Use Volume Calculator?
Please follow the below steps to find the volume using the online volume calculator:
- Step 1: Go to Cuemath’s online volume calculator.
- Step 2: Choose the shape from the drop-down list and enter the values in the input box of the volume calculator.
- Step 3: Click on the "Calculate" button to find the volume.
- Step 4: Click on the "Reset" button to clear the fields and enter new values.
How does Volume Calculator work?
Depending upon the shape there are a number of different formulas available to calculate volume. The base area multiplied by the height gives the volume of most shapes.
1. Volume of a cuboid: A cuboid is a three-dimensional shape that is made up of 6 quadrilateral faces. The formula to calculate the volume of a cuboid is:
The volume of a cuboid = Base Area × Height = l × b × h.
The base area of a cuboid is a rectangle which is l × b.
Where 'l' is the base length, 'b' is the base width, and 'h' is the height of the cuboid.
2. Volume of the cube: A cube can be thought of as a special case of a cuboid that has all equal sides.The formula to calculate the volume of the cube is:
The volume of a cube = a3.
The base area is a square given by a2.
Where 'a' is the side of the cube.
3. Volume of a cylinder: A cylinder has two parallel circular bases and is joined by a curved surface to form a tube-like structure. The formula to calculate the volume of a cylinder is:
Volume of a cylinder = πr2h.
The base area of a cylinder is a circle which is πr2.
Where r is the radius, h is the height, and π(Pi) is a mathematical constant with an approximate value of 3.14 or 22/7.
4. Volume of a cone: A cone has a circular base with triangular faces that meet at its apex. The formula to calculate the volume of a cone is:
The volume of a cone = (1/3)πr2h.
The base area of a cone is a circle which is πr2.
Where 'r' is the radius and 'h' is the height of a cone.
5. Volume of a sphere: A sphere is a geometric shape that resembles a ball. The formula to calculate the volume of a sphere is:
The volume of a sphere = 4/3 × π × r3.
Where 'r' is the radius of the sphere.
6. Volume of a triangular prism: A triangular prism has two triangular bases with three faces joining the sides. The formula to calculate the volume of a triangular prism is:
The volume of triangular prism = Base Area × height of the prism = 1/2 × (b × h) × l.
Where 'b' is base length, and 'h' is the height, and 'l' is the distance between the bases or height of the triangle of the prism.
7. Volume of a triangular pyramid: A triangular pyramid has a triangular base and triangular faces that meet at the apex. The formula to calculate the volume of a triangular pyramid is:
The volume of a triangular pyramid = 1/3 × Base Area of triangle × Height of pyramid.
Note: Base area of a triangle is 1/2 × base width of triangle × base height of the triangle.
Solved Examples on Volume Calculator
Example 1:
Find the volume of a cube if the length of the side is 9 units and verify it using the volume calculator.
Solution:
The formula used to find the volume of a cube = a3 cubic units
= (9)3 cubic units.
= 9 × 9 × 9 cubic units.
=729 cubic units.
Example 2:
Find the volume of a cone whose height = 3 units and radius = 7 units.
Solution:
When the height and radius are given, we can use the formula to calculate the volume of a cone.
Volume = (1/3)πr²h
=(1/3)π × 7² × 3
=153.86 cubic units
Similarly, you can try the calculator to find the volume using an online volume calculator for the following:
- Find the volume of a cuboid if the base length of the cuboid is 5 units, the base width of the cuboid is 6 units, and the height of the cuboid is 7 units.
- Find the volume of a triangular pyramid with a base width of a triangle of 5 units, the base height of a triangle is 6 units, and the height of the pyramid is 9 units.