Volume and capacity: Overview and Sample Questions

Volume and capacity are both interrelated terms and have very close meanings. Volume is defined as the space or area which is occupied by any substance, and capacity refers to the quantity of a substance that could be stored in another hollow object. For example, a ball has some volume, and a bottle has 1 liter of capacity. The article below gives an overview of the topic volume and capacity with some sample questions. 

Keywords: Volume, Capacity, Shapes, Cube, Cuboid, Sphere, Cylinder, Cone, Mass, etc.

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What are Volume & Capacity

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Volume and capacity are both interrelated terms and have very close meanings. Volume is defined as the space or area which is occupied by any substance, for example, a cube occupies a certain volume. Whereas, capacity refers to the volume of the substance which can be stored in another vessel. For example, in a hollow cylinder, one can store water, and the amount of water that can be stored in the cylinder tells us its capacity. The capacity is also determined by calculating its volume.

Volume is calculated for three-dimensional structures. The three-dimensional structures are characterized by the presence of three parameters, which are used to calculate its volume or capacity, they are:

1. Length: This is the measurement of an edge from one corner to another. This is the longest of the three dimensions.
2. Breadth: This is the measurement of an edge from one corner to another. This is the shortest of the three dimensions.
3. Height: This is the measurement of an edge from one corner to another. This is the vertical edge of the three dimensions.

Volume is determined in cubic units, i.e., unit3. These units can be meters (m³), centimeters (cm³), kilometers (km³), etc. In order to calculate the volume of a few shapes, like cubes and cuboids, the entire structure can be divided into smaller cubes, since cubes have the same length, breadth, and height.

Capacity, which also represents volume, can be represented in Liters. Liters can be co-related to several other units, like, 1 L = 1000 cm3, 1 mL = 1 cm3, etc. Thus, 1 m3 = 1000000 cm3 = 1000 L.

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The Volume of Common Shapes

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There are several common shapes and structures surrounding us, and they all occupy some mass and volume. The formula to calculate the volume of a few common shapes is given below.

Cube

A cube is a three-dimensional structure having six faces and twelve edges. It is the three-dimensional structure for a square and has equal length, breadth, and height. Thus, all these three dimensions can be called sides here. The volume of a cube can be determined by measuring the value of any one of its edges. Thus

Volume of a cube = length X breadth X height

Here, length = breadth = height, thus,

Volume of a cube = side X side X side

Volume of a cube = side³ 

Cuboid

A cuboid is also a three-dimensional structure having six faces and twelve edges. It is the three-dimensional structure for a rectangle and has unequal length, breadth, and height. The volume of a cuboid can be determined by measuring the value of all of its edges. Thus

Volume of a cuboid = length X breadth X height

Sphere

A sphere is a three-dimensional structure. It is a 3-D structure for a circle, which is composed of several circles placed together. Like a circle, the sphere also possesses a center and a radius. And its radius is used to determine its volume.

The volume of a solid sphere = 4/3 π r³

r = radius of the sphere

Cylinder

A cylinder is a three-dimensional structure, composed of two circular faces, and one curved surface holding the two circular faces at two ends. The curved surface has a uniform height throughout. Here, the radius of the circular face, and the height/length of the curved surface.

The volume of a cylinder = π r² h

r = radius of the circular surface

h = length of the curved surface.

Cone

A cone is a three-dimensional structure resembling a triangle. Here, it has one circular surface with a curved surface that keeps decreasing in width and ends into a point at the top. In order to determine the volume of a cone, we need to calculate the values of the radius of the base, the perpendicular height of the cone, and its slant length too.

The volume of a cone = 1/3 π r² h

r = radius of the circular surface

h = perpendicular height of the cone.

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Things to Remember

1. Volume is defined as the space or area which is occupied by any substance.
2. Capacity refers to the volume of the substance which can be stored in another vessel.
3. The capacity is also determined by calculating its volume.
4. Volume of a cube = side³
5. Volume of a cuboid = length X breadth X height
6. The volume of a solid sphere = 4/3 π r³, r = radius of the sphere
7. The volume of a cylinder = π r² h
8. The volume of a cone = 1/3 π r² h
9. The volume is always represented in cubic units.
10. 1 L = 1000 cm³, 1 mL = 1 cm³, etc. Thus, 1 m³ = 1000000 cm³ = 1000 L.

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