How to find the volume using the area and height?

Mensuration is the part of mathematics that deals with studying various geometrical shapes, their areas, and volume. In simple terms, mensuration is all about measurement. The measurement of various body dimensions and calculation of area, surface area, and volume are studied under mensuration. 

Volume

Volume is defined as a 3-dimensional space that is closed or bound by an object. Finding the volume of an object can help us to determine the quantity needed to fill an object, such as the water needed to fill a bottle, a swimming pool, or a water tank. The volume of an object is estimated in cubic units such as cubic centimeters, cubic inch, cubic foot, cubic meter, etc.

The volume of most objects can be easily calculated given the base area and height, even complex ones. The complex objects can be segmented into simpler figures, and thus adding the volumes of these simpler figures can be summed to obtain the volume of the entire object.

How to find the volume using the area and height?

In order to find the volume of a given object, it can be done in the following ways,

1. Find the base area
2. Multiply the base area with the corresponding height.

Calculating the volume of some familiar figures,

Cube

A cube is a three-dimensional object that has six congruent square faces. Dimensions of all the 6 square faces of the cube are identical. A cube is seldom also ascribed to as a regular hexahedron or as a square prism.

The base area of a cube = side × side

Height of the cube = side

Volume of the cube = base area × height = side³

Cuboid

A cuboid is a three-dimensional solid shape that has six faces, eight vertices, and 12 edges. It is one of the common shapes around us, which has three dimensions: length, width, and height.

The base area of the cuboid = Length × Breadth

Height of the cuboid = Depth

Volume of the cuboid = base area × height = Length × Breadth × Depth

Cylinder

A cylinder is a three-dimensional solid figure in geometry, which has two parallel circular bases bounded by a curved surface at a precise distance from the center. Candles, batteries are real-life examples of cylinders. 

The base area of a cylinder = 3.14 × R²

Height of the cylinder = Length

Volume of the cylinder = base area x height = 3.14 × R² × Length

Sample Problems

Question 1: The base area of a cube is 25 cm², and the height is 5 cm.  Find the volume.

Solution:

Volume = base area × height 

= 25 × 5

= 125 cm³

Question 2: The base area of a cuboid is 10 cm², and the height is 50 cm.  Find the volume.

Solution:

Volume = base area × height

 = 10 x 50

 = 500 cm³

Question 3: The base area of a cylinder is 30  cm², and its length is 10 cm.  Find its volume.

Solution:

Volume = base area × height

 = 30 × 10

 = 300 cm²