# 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 cm^{3} of water up to the brim. Then the volume of the bottle will be 50cm^{3}. 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 = a^{3}.

The base area is a square given by a^{2}.

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 = πr^{2}h.

The base area of a cylinder is a circle which is πr^{2}.

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)πr^{2}h.

The base area of a cone is a circle which is πr^{2}.

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 × r^{3}.

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

**Example1:** 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 = a^{3 }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.

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