About Area Vs Volume
Area and Volume
The area of a two-dimensional object is calculated but the volume cannot be calculated. However, the volume of a three-dimensional object can be calculated, as well as the area of its faces can also be calculated.
What is Area?
The measure of the region covered by a two-dimensional shape is known as the area. It is measured in square units such as square inches, square feet, and so on.
Circles, triangles, squares, rectangles, parallelograms, pentagons, and hexagons are examples of two-dimensional shapes. The formula for the calculation of the area of each shape depends on the shape itself. As a result, each of these shapes have a different formula to calculate the area.
What is Volume?
Volume is the space occupied by a solid. Volume is attributed only to three-dimensional objects. The formula to calculate the volume of each solid, such as a sphere, a cube, a cuboid, a cylinder, a cone, and so on, depends on the solid. Cubic units are used to measure it such as cubic feet, cubic inches, and so on.
Rapid Recall
What is the distinction between volume and area?
Area | Volume |
|---|---|
The area of a two-dimensional flat object is the measure of the region covered by the object. | A three-dimensional object's volume is defined as the amount of space it takes up. |
In two dimensional objects, the area can be calculated, but the volume cannot be calculated. | In three dimensional objects, volume is calculated. In addition, the area of each face can also be calculated, as each face of a solid is a two-dimensional figure. |
Area is measured in square units. | Volume is measured in cubic units. |
Area is generally measured using two dimensions of a shape which are: length and width. | Volume is measured using the three dimensions of the solid which are: length, width and height. |
Solved Area & Volume Examples
Example 1: The side of a square plot is 7 meter. Calculate the area of the square plot.
Solution:
It is given that, the side of the square plot, a = 7 meters
The formula for calculating the area of a square, A = a\( ^2 \)
A = 7 × 7
A = 49 square meters
Therefore, the area of the square plot is 49 square meters.
Example 2: The side length of a cubic box is 9 inches long. Calculate the volume of the cubic box.
Solution:
It is given that, the side of the cubic box, a = 9 inches
The formula of volume of a cube, V = a\( ^3 \)
V = 9 × 9 × 9
V = 729 cubic inches.
Therefore, the volume of the cubic box is 729 cubic inches.
Example 3: Calculate the volume of a conical vessel with a radius of 7 inches radius and a height of 9 inches. You are given the value of \( \pi \) as \( \frac{22}{7} \).
Solution:
The vessel is shaped as a cone.
The formula of volume of cone \( =\frac{1}{3}\pi r^2h \)
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 9 \)
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=462 \) cubic inches
As a result, the vessel’s volume is 462 cubic inches.
The area is the measure of the region of a two-dimensional shape, while the perimeter is the measure of the distance around the shape (its boundary), and the volume is the capacity of a given three-dimensional shape.
The area of a circle is the amount of region that the circle takes up in a two-dimensional plane. In other words, it is the area occupied within the circle’s boundary. The formula for calculating the area of a circle is \( A=\pi r^2 \), where r is the radius of the circle.
Area is typically measured in square units such as square meters, square feet, square inches and other units related to measuring the area of a two dimensional shape or the surface area of a solid shape. In the case of calculating volume, it is typically measured in cubic units, such as cubic feet, cubic inches, cubic meters and so on.
No, area and volume are not the same. Volume is measured only for three-dimensional objects, and not for two-dimensional objects, whereas, area is measured only for two-dimensional figures.